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<h2> <a href="science.html"> ⇦ Back to Science chapter list</a></h2>
<section class="sv-section">
<h1>Electrodynamics</h1>
<section class="sv-section">
<h2>1. Introduction</h2>
</section> <section class="sv-section">
<h2>2. Electrical machines - generators and motors</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id2388-5798">ID is: 2388 Seed is: 5798<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">AC and DC generators</h3>
</span><div class="problem">
<p>
Are the following statements true or false?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<ol>
<li> DC generators are safe to be used in environments with an increased fire risk. <br><select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">True</option><option value="1" selected="">False</option></select> </li>
<li> An AC generator has one slip ring to connect the rotating coil to the external circuit. <br><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
<li> A generator converts electrical energy into mechanical energy. <br><select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
<li> A DC generator has two slip rings to connect the rotating coil to the external circuit. <br><select name="question1d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
</ol>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:15.621093"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id2388-6479">ID is: 2388 Seed is: 6479<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">AC and DC generators</h3>
</span><div class="problem">
<p>
Are the following statements true or false?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<ol>
<li> A DC generator has two split ring commutators to connect the rotating coil to the external circuit. <br><select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
<li> A generator converts electrical energy into mechanical energy. <br><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
<li> An AC generator has a split ring commutator to connect the rotating coil to the external circuit. <br><select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
<li> DC generators are safe to be used in environments with an increased fire risk. <br><select name="question1d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">False</option><option value="0">True</option></select> </li>
</ol>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:15.637357"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id4039-9687">ID is: 4039 Seed is: 9687<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST"><span class="worked_example"><h3 class="sv-heading">Electrical machines</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from WCED Metro Central Sep 2017 Grade 12, P1, Q9.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The diagram below represents part of a certain type of motor as seen from above. The side of the coil marked <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mi" id="MathJax-Span-3" style="font-family: STIXGeneral; font-style: italic;">𝑊<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-4" style="font-family: STIXGeneral; font-style: italic;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-1">WX</script></span> is moving <strong>into the page</strong>, and the side marked <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mi>Z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-5" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.52em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-6"><span class="mi" id="MathJax-Span-7" style="font-family: STIXGeneral; font-style: italic;">𝑌<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-8" style="font-family: STIXGeneral; font-style: italic;">𝑍<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mi>Z</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">YZ</script></span> is moving <strong>out of the page</strong>. The magnetic poles are indicated. Study the diagram and answer the questions that follow.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4039/9687/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0"></a></div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
State the energy conversion that takes place inside a motor.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
In a motor, <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">electrical</option><option value="1">mechanical</option><option value="2">chemical</option><option value="3">magnetic</option></select> energy is converted to <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">electrical</option><option value="1" selected="">mechanical</option><option value="2">chemical</option><option value="3">magnetic</option></select> energy.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
When the coil is in the position shown in the diagram, what is the direction of conventional current in segment <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-9" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-10"><span class="mi" id="MathJax-Span-11" style="font-family: STIXGeneral; font-style: italic;">𝑊<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-12" style="font-family: STIXGeneral; font-style: italic;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">WX</script></span>?</span>
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The conventional current in segment <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-13" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-14"><span class="mi" id="MathJax-Span-15" style="font-family: STIXGeneral; font-style: italic;">𝑊<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-16" style="font-family: STIXGeneral; font-style: italic;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">WX</script></span> will flow <select name="question2a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">up</option><option value="1">down</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
Other than carbon brushes, identify <strong>two</strong> components required in the rest of circuit that will make the above motor a DC motor.
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The circuit will need <select name="question3a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="3">slit rings</option><option value="2">a slip-ring commutator</option><option value="0">slip rings</option><option value="1" selected="">a commutator</option></select> and <select name="question3b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">a load</option><option value="3">an ammeter</option><option value="2">a voltmeter</option><option value="0" selected="">a DC power source</option></select>.
</div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:52:15.662715"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id4039-5447">ID is: 4039 Seed is: 5447<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST"><span class="worked_example"><h3 class="sv-heading">Electrical machines</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from WCED Metro Central Sep 2017 Grade 12, P1, Q9.1</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The diagram below represents part of a certain type of generator as seen from above. The side of the coil marked <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-17" style="width: 2.286em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.88em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-18"><span class="mi" id="MathJax-Span-19" style="font-family: STIXGeneral; font-style: italic;">𝑊<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-20" style="font-family: STIXGeneral; font-style: italic;">𝑋<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mi>X</mi></math></span></span><script type="math/tex" id="MathJax-Element-5">WX</script></span> is moving <strong>out of the page</strong>, and the side marked <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mi>Z</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-21" style="width: 1.876em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.525em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1001.52em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-22"><span class="mi" id="MathJax-Span-23" style="font-family: STIXGeneral; font-style: italic;">𝑌<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span class="mi" id="MathJax-Span-24" style="font-family: STIXGeneral; font-style: italic;">𝑍<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mi>Z</mi></math></span></span><script type="math/tex" id="MathJax-Element-6">YZ</script></span> is moving <strong>into the page</strong>. The magnetic poles are indicated. Study the diagram and answer the questions that follow.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4039/5447/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(1)"></a></div>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
State the energy conversion that takes place inside a generator.
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
In a generator, <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">chemical</option><option value="1">magnetic</option><option value="2" selected="">mechanical</option><option value="3">electrical</option></select> energy is converted to <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">chemical</option><option value="1">magnetic</option><option value="2">mechanical</option><option value="3" selected="">electrical</option></select> energy.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
When the coil is in the position shown in the diagram, which side of the coil will have conventional current moving <strong>to the left</strong> through it?
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The side of the coil with conventional current moving to the left is <select name="question2a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">WX</option><option value="1" selected="">YZ</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
Other than carbon brushes, identify <strong>two</strong> components required in the rest of circuit that will make the above generator a DC generator.
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
The circuit will need <select name="question3a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1" selected="">a commutator</option><option value="0">slip rings</option><option value="2">a slip-ring commutator</option><option value="3">slit rings</option></select> and <select name="question3b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="1">a Galvanic cell</option><option value="0" selected="">a voltmeter</option><option value="3">a DC adapter</option><option value="2">a DC power source</option></select>.
</div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:52:15.693262"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2327-4934">ID is: 2327 Seed is: 4934<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Induced current of a coil rotating in a magnetic field</h3>
</span><div class="problem">
<p>
The diagram below shows a circular coil rotating counter-clockwise in a uniform magnetic field. The first figure at the top left shows the coil oriented so that <strong>the normal to the coil</strong> is at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>135</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-25" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-26"><span class="mi" id="MathJax-Span-27" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-28" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-29" style="font-family: STIXGeneral; padding-left: 0.296em;">135</span><span class="mtext" id="MathJax-Span-30" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-31"><span class="mrow" id="MathJax-Span-32"><span class="mo" id="MathJax-Span-33" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>135</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-7">\theta = \text{135}~°</script></span> with respect to the direction of the magnetic field. The second figure shows the coil at an angle of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>180</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-34" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-35"><span class="mi" id="MathJax-Span-36" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-37" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-38" style="font-family: STIXGeneral; padding-left: 0.296em;">180</span><span class="mtext" id="MathJax-Span-39" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-40"><span class="mrow" id="MathJax-Span-41"><span class="mo" id="MathJax-Span-42" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>180</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-8">\theta = \text{180}~°</script></span>,</span> and the third shows the coil at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>225</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-43" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-44"><span class="mi" id="MathJax-Span-45" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-46" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-47" style="font-family: STIXGeneral; padding-left: 0.296em;">225</span><span class="mtext" id="MathJax-Span-48" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-49"><span class="mrow" id="MathJax-Span-50"><span class="mo" id="MathJax-Span-51" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>225</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-9">\theta = \text{225}~°</script></span> with respect to the uniform magnetic field.
</p>
<p>
The four graphs <strong>(A, B, C, and D)</strong> on the right shows four options for the induced current, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-52" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-53"><span class="mi" id="MathJax-Span-54" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span><script type="math/tex" id="MathJax-Element-10">I</script></span> plotted against the angle of the coil, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-55" style="width: 0.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-56"><span class="mi" id="MathJax-Span-57" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">\theta</script></span>.</span>
</p>
<p>
Study the diagram, and answer the question that follows:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2327/4934/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(2)"></a></div>
<p>
Which graph <strong>(A, B, C, or D)</strong> represents the correct induced current versus angle graph (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext>&#xA0;</mtext><mtext>vs.</mtext><mtext>&#xA0;</mtext><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-58" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-59"><span class="mi" id="MathJax-Span-60" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span class="mtext" id="MathJax-Span-61" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-62" style="font-family: STIXGeneral;">vs.</span><span class="mtext" id="MathJax-Span-63" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-64" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext> </mtext><mtext>vs.</mtext><mtext> </mtext><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-12">I~ \text{vs.} ~\theta</script></span>) for the positions of the coil as shown in the diagram on the left?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">Graph A</option><option value="1">Graph B</option><option value="2">Graph C</option><option value="3">Graph D</option></select> represents the correct induced current versus angle graph (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext>&#xA0;</mtext><mtext>vs.</mtext><mtext>&#xA0;</mtext><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-65" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-66"><span class="mi" id="MathJax-Span-67" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span class="mtext" id="MathJax-Span-68" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-69" style="font-family: STIXGeneral;">vs.</span><span class="mtext" id="MathJax-Span-70" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-71" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext> </mtext><mtext>vs.</mtext><mtext> </mtext><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-13">I~ \text{vs.} ~\theta</script></span>) for the positions of the coil as shown in the diagram.
</p>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2327-7875">ID is: 2327 Seed is: 7875<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Induced current of a coil rotating in a magnetic field</h3>
</span><div class="problem">
<p>
The diagram below shows a circular coil rotating counter-clockwise in a uniform magnetic field. The first figure at the top left shows the coil oriented so that <strong>the normal to the coil</strong> is at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>180</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-72" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-73"><span class="mi" id="MathJax-Span-74" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-75" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-76" style="font-family: STIXGeneral; padding-left: 0.296em;">180</span><span class="mtext" id="MathJax-Span-77" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-78"><span class="mrow" id="MathJax-Span-79"><span class="mo" id="MathJax-Span-80" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>180</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-14">\theta = \text{180}~°</script></span> with respect to the direction of the magnetic field. The second figure shows the coil at an angle of <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>225</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-81" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-82"><span class="mi" id="MathJax-Span-83" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-84" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-85" style="font-family: STIXGeneral; padding-left: 0.296em;">225</span><span class="mtext" id="MathJax-Span-86" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-87"><span class="mrow" id="MathJax-Span-88"><span class="mo" id="MathJax-Span-89" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>225</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-15">\theta = \text{225}~°</script></span>,</span> and the third shows the coil at an angle of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi><mo>=</mo><mtext>270</mtext><mtext>&#xA0;</mtext><mrow class="MJX-TeXAtom-ORD"><mo>&#xB0;</mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-90" style="width: 4.804em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.926em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.87em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-91"><span class="mi" id="MathJax-Span-92" style="font-family: STIXGeneral; font-style: italic;">𝜃</span><span class="mo" id="MathJax-Span-93" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-94" style="font-family: STIXGeneral; padding-left: 0.296em;">270</span><span class="mtext" id="MathJax-Span-95" style="font-family: STIXGeneral;"> </span><span class="texatom" id="MathJax-Span-96"><span class="mrow" id="MathJax-Span-97"><span class="mo" id="MathJax-Span-98" style="font-family: STIXGeneral;">°</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mtext>270</mtext><mtext> </mtext><mrow class="MJX-TeXAtom-ORD"><mo>°</mo></mrow></math></span></span><script type="math/tex" id="MathJax-Element-16">\theta = \text{270}~°</script></span> with respect to the uniform magnetic field.
</p>
<p>
The four graphs <strong>(A, B, C, and D)</strong> on the right shows four options for the induced current, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-99" style="width: 0.647em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.53em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.53em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-100"><span class="mi" id="MathJax-Span-101" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span><script type="math/tex" id="MathJax-Element-17">I</script></span> plotted against the angle of the coil, <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-102" style="width: 0.588em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.471em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.47em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-103"><span class="mi" id="MathJax-Span-104" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-18">\theta</script></span>.</span>
</p>
<p>
Study the diagram, and answer the question that follows:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2327/7875/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(3)"></a></div>
<p>
Which graph <strong>(A, B, C, or D)</strong> represents the correct induced current versus angle graph (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext>&#xA0;</mtext><mtext>vs.</mtext><mtext>&#xA0;</mtext><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-105" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-106"><span class="mi" id="MathJax-Span-107" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span class="mtext" id="MathJax-Span-108" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-109" style="font-family: STIXGeneral;">vs.</span><span class="mtext" id="MathJax-Span-110" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-111" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext> </mtext><mtext>vs.</mtext><mtext> </mtext><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-19">I~ \text{vs.} ~\theta</script></span>) for the positions of the coil as shown in the diagram on the left?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">Graph A</option><option value="1">Graph B</option><option value="2" selected="">Graph C</option><option value="3">Graph D</option></select> represents the correct induced current versus angle graph (<span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext>&#xA0;</mtext><mtext>vs.</mtext><mtext>&#xA0;</mtext><mi>&#x03B8;</mi></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-112" style="width: 3.223em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.638em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.64em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-113"><span class="mi" id="MathJax-Span-114" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span class="mtext" id="MathJax-Span-115" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-116" style="font-family: STIXGeneral;">vs.</span><span class="mtext" id="MathJax-Span-117" style="font-family: STIXGeneral;"> </span><span class="mi" id="MathJax-Span-118" style="font-family: STIXGeneral; font-style: italic;">𝜃</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mtext> </mtext><mtext>vs.</mtext><mtext> </mtext><mi>θ</mi></math></span></span><script type="math/tex" id="MathJax-Element-20">I~ \text{vs.} ~\theta</script></span>) for the positions of the coil as shown in the diagram.
</p>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2387-4053">ID is: 2387 Seed is: 4053<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Alternating current and direct current</h3>
</span><div class="problem">
<p>
Which of the following graphs correctly shows the current vs. time graph for an AC generator?
</p>
<table border="1">
<tbody><tr>
<td>
<strong>A</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4053/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(4)"></a></div>
</td>
</tr>
<tr>
<td>
<strong>B</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4053/1"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/1"></a></div>
</td>
</tr>
<tr>
<td>
<strong>C</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4053/2"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/2"></a></div>
</td>
</tr>
<tr>
<td>
<strong>D</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4053/3"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/3"></a></div>
</td>
</tr>
</tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2" selected="">C</option><option value="3">D</option></select>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2387-4590">ID is: 2387 Seed is: 4590<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Alternating current and direct current</h3>
</span><div class="problem">
<p>
Which of the following graphs correctly shows the current vs. time graph for a DC generator?
</p>
<table border="1">
<tbody><tr>
<td>
<strong>A</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4590/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(5)"></a></div>
</td>
</tr>
<tr>
<td>
<strong>B</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4590/1"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/1(1)"></a></div>
</td>
</tr>
<tr>
<td>
<strong>C</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4590/2"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/2(1)"></a></div>
</td>
</tr>
<tr>
<td>
<strong>D</strong>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2387/4590/3"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/3(1)"></a></div>
</td>
</tr>
</tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option><option value="3">D</option></select>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id3843-951">ID is: 3843 Seed is: 951<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Multiple choice: Generators and motors</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q1.9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
In a DC generator the current to the external circuit (the load) is delivered through the ...
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td>power source.</td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>magnets.</td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>slip rings.</td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>split rings (commutators).</td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2">C</option><option value="3" selected="">D</option></select>
</div></div></div>
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<span class="worked_example"><h3 class="sv-heading">Multiple choice: Generators and motors</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q1.9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
In an AC generator the current to the external circuit (the load) is delivered through the ...
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td>cell.</td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td>coils.</td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td>slip rings.</td></tr><tr> <td style="background:lightgray"><strong>D</strong></td> <td>split rings (commutators).</td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2" selected="">C</option><option value="3">D</option></select>
</div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2322-4312">ID is: 2322 Seed is: 4312<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Right hand rule</h3>
</span><div class="problem">
<p>
Identify which physical quantity is represented by each finger (A, B and C) as proposed by Fleming's right hand rule for generators.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2322/4312/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(6)"></a></div>
<p>
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p align="center">
</p><table border="1" width="400">
<tbody><tr><th align="center">Finger</th><th align="center">Physical Quantity</th></tr>
<tr><td align="center">A.</td><td align="center"><select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">Force (F)</option><option value="1">Magnetic Field (B)</option><option value="2">Induced Current (I)</option></select></td></tr>
<tr><td align="center">B.</td><td align="center"><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">Force (F)</option><option value="1" selected="">Magnetic Field (B)</option><option value="2">Induced Current (I)</option></select></td></tr>
<tr><td align="center">C.</td><td align="center"><select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">Force (F)</option><option value="1">Magnetic Field (B)</option><option value="2" selected="">Induced Current (I)</option></select></td></tr>
</tbody></table>
<p></p>
</div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2322-9458">ID is: 2322 Seed is: 9458<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Right hand rule</h3>
</span><div class="problem">
<p>
Identify which physical quantity is represented by each finger (A, B and C) as proposed by Fleming's right hand rule for generators.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/2322/9458/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(7)"></a></div>
<p>
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p align="center">
</p><table border="1" width="400">
<tbody><tr><th align="center">Finger</th><th align="center">Physical Quantity</th></tr>
<tr><td align="center">A.</td><td align="center"><select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">Force (F)</option><option value="1" selected="">Magnetic Field (B)</option><option value="2">Induced Current (I)</option></select></td></tr>
<tr><td align="center">B.</td><td align="center"><select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">Force (F)</option><option value="1">Magnetic Field (B)</option><option value="2" selected="">Induced Current (I)</option></select></td></tr>
<tr><td align="center">C.</td><td align="center"><select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">Force (F)</option><option value="1">Magnetic Field (B)</option><option value="2">Induced Current (I)</option></select></td></tr>
</tbody></table>
<p></p>
</div></div></div>
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</div></section></section> <section class="sv-section">
<h2>3. Alternating current</h2>
<hr><section class="sv-section sv-question sv-table"><br><div class="id2326-7976">ID is: 2326 Seed is: 7976<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Electrodynamic properties of appliances: maximum current</h3>
</span><div class="problem">
<p>
A designer is investigating the electrodynamic properties of a handheld blender.
</p>
<p>
The figure on the right shows a simplified circuit diagram of the handheld blender.
</p>
<p>
</p><div class="figure"><a href="https://www.emas.com/practice/isolated_image/2326/7976/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(8)"></a></div>
<p></p>
<p>
The designer has determined the root mean square value of the alternating current supplied to the handheld blender as <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo><mtext>1,2</mtext><mtext>&#xA0;</mtext><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-119" style="width: 6.326em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.155em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1005.15em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-120"><span class="msubsup" id="MathJax-Span-121"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-122" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-123"><span class="mrow" id="MathJax-Span-124"><span class="mi" id="MathJax-Span-125" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-126" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-127" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-128" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-129" style="font-family: STIXGeneral; padding-left: 0.296em;">1,2</span><span class="mtext" id="MathJax-Span-130" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-131" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo><mtext>1,2</mtext><mtext> </mtext><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-21">I_{rms} = \text{1,2}\ \text{A}</script></span>.</span>
</p>
<p>
What is the <strong>maximum value</strong> of the alternating current supplied to the handheld blender, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-132" style="width: 2.228em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.82em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-133"><span class="msubsup" id="MathJax-Span-134"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-135" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-136"><span class="mrow" id="MathJax-Span-137"><span class="mi" id="MathJax-Span-138" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-139" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-140" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-22">I_{max}</script></span>?</span>
</p>
<ul>
<li>round your answer to <strong>two decimal places</strong></li>
<li>use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a></li>
</ul>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-141" style="width: 3.457em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.813em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.75em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-142"><span class="msubsup" id="MathJax-Span-143"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-144" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-145"><span class="mrow" id="MathJax-Span-146"><span class="mi" id="MathJax-Span-147" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-148" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-149" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-150" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-23">I_{max} = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1,7" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-151" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-152"><span class="mtext" id="MathJax-Span-153" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-24">\text{A}</script></span><div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2326-1806">ID is: 2326 Seed is: 1806<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Electrodynamic properties of appliances: maximum current</h3>
</span><div class="problem">
<p>
An engineer is investigating the electrodynamic properties of a coffee maker.
</p>
<p>
The figure on the right shows a simplified circuit diagram of the coffee maker.
</p>
<p>
</p><div class="figure"><a href="https://www.emas.com/practice/isolated_image/2326/1806/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(9)"></a></div>
<p></p>
<p>
The engineer has determined the root mean square value of the alternating current supplied to the coffee maker as <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo><mtext>7,56</mtext><mtext>&#xA0;</mtext><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-154" style="width: 6.853em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.624em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1005.62em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-155"><span class="msubsup" id="MathJax-Span-156"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-157" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-158"><span class="mrow" id="MathJax-Span-159"><span class="mi" id="MathJax-Span-160" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-161" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-162" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-163" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-164" style="font-family: STIXGeneral; padding-left: 0.296em;">7,56</span><span class="mtext" id="MathJax-Span-165" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-166" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo><mtext>7,56</mtext><mtext> </mtext><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-25">I_{rms} = \text{7,56}\ \text{A}</script></span>.</span>
</p>
<p>
What is the <strong>maximum value</strong> of the alternating current supplied to the coffee maker, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-167" style="width: 2.228em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.82em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-168"><span class="msubsup" id="MathJax-Span-169"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-170" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-171"><span class="mrow" id="MathJax-Span-172"><span class="mi" id="MathJax-Span-173" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-174" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-175" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-26">I_{max}</script></span>?</span>
</p>
<ul>
<li>round your answer to <strong>two decimal places</strong></li>
<li>use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a></li>
</ul>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-176" style="width: 3.457em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.813em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.75em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-177"><span class="msubsup" id="MathJax-Span-178"><span style="display: inline-block; position: relative; width: 1.818em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-179" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-180"><span class="mrow" id="MathJax-Span-181"><span class="mi" id="MathJax-Span-182" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-183" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-184" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-185" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-27">I_{max} = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="10,69" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-186" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-187"><span class="mtext" id="MathJax-Span-188" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-28">\text{A}</script></span><div class="response-type">numeric</div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:15.933762"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id3718-9614">ID is: 3718 Seed is: 9614<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST"><span class="worked_example"><h3 class="sv-heading">Understanding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-189" style="width: 7.73em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.325em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.758em, 1006.33em, 2.968em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-190"><span class="msubsup" id="MathJax-Span-191"><span style="display: inline-block; position: relative; width: 1.68em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.71em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-192" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.119em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-193"><span class="mrow" id="MathJax-Span-194"><span class="mtext" id="MathJax-Span-195" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span><span class="mo" id="MathJax-Span-196" style="font-family: STIXGeneral; padding-left: 0.314em;">=</span><span class="msubsup" id="MathJax-Span-197" style="padding-left: 0.314em;"><span style="display: inline-block; position: relative; width: 1.719em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.74em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-198" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.197em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-199"><span class="mrow" id="MathJax-Span-200"><span class="mtext" id="MathJax-Span-201" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-202"><span style="display: inline-block; position: relative; width: 1.602em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.55em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-203" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.041em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.47em;"><span class="texatom" id="MathJax-Span-204"><span class="mrow" id="MathJax-Span-205"><span class="mtext" id="MathJax-Span-206" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.426em; border-left: 0px solid; width: 0px; height: 1.288em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-29">P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}}</script></span> </h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
The relationship <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-207" style="width: 7.731em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.326em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1006.33em, 2.989em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-208"><span class="msubsup" id="MathJax-Span-209"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-210" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-211"><span class="mrow" id="MathJax-Span-212"><span class="mtext" id="MathJax-Span-213" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-214" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-215" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-216" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-217"><span class="mrow" id="MathJax-Span-218"><span class="mtext" id="MathJax-Span-219" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-220"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-221" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-222"><span class="mrow" id="MathJax-Span-223"><span class="mtext" id="MathJax-Span-224" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-30">P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}}</script></span> is a useful equation when working with electric circuits.
</p>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
What does the symbol <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-225" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-226"><span class="msubsup" id="MathJax-Span-227"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-228" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-229"><span class="mrow" id="MathJax-Span-230"><span class="mtext" id="MathJax-Span-231" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-31"> P_{\text{avg}}</script></span> represent?
</p>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The symbol <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-232" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-233"><span class="msubsup" id="MathJax-Span-234"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-235" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-236"><span class="mrow" id="MathJax-Span-237"><span class="mtext" id="MathJax-Span-238" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-32">P_{\text{avg}}</script></span> represents the <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">average</option><option value="1">root mean square</option><option value="2">maximum</option><option value="3">minimum</option></select> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">impedance</option><option value="1">current</option><option value="2" selected="">power</option><option value="3">pressure</option><option value="4">potential difference</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
What is the SI unit used to measure <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-239" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.64em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-240"><span class="msubsup" id="MathJax-Span-241"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-242" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-243"><span class="mrow" id="MathJax-Span-244"><span class="mtext" id="MathJax-Span-245" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-33">I_{\text{rms}}</script></span>?</span>
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The SI unit used to measure <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-246" style="width: 1.994em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.64em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-247"><span class="msubsup" id="MathJax-Span-248"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-249" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-250"><span class="mrow" id="MathJax-Span-251"><span class="mtext" id="MathJax-Span-252" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-34">I_{\text{rms}}</script></span> is <select name="question2a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">A</option><option value="1">N</option><option value="2">W</option><option value="3">V</option><option value="4">Hz</option></select>.
</p>
</div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:52:15.960229"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><section class="sv-section sv-question sv-table"><br><div class="id3718-3071">ID is: 3718 Seed is: 3071<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST"><span class="worked_example"><h3 class="sv-heading">Understanding <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-253" style="width: 7.73em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.325em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.758em, 1006.33em, 2.968em, -999.998em); top: -2.535em; left: 0em;"><span class="mrow" id="MathJax-Span-254"><span class="msubsup" id="MathJax-Span-255"><span style="display: inline-block; position: relative; width: 1.68em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.71em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-256" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.119em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-257"><span class="mrow" id="MathJax-Span-258"><span class="mtext" id="MathJax-Span-259" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span><span class="mo" id="MathJax-Span-260" style="font-family: STIXGeneral; padding-left: 0.314em;">=</span><span class="msubsup" id="MathJax-Span-261" style="padding-left: 0.314em;"><span style="display: inline-block; position: relative; width: 1.719em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.74em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-262" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.197em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-263"><span class="mrow" id="MathJax-Span-264"><span class="mtext" id="MathJax-Span-265" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-266"><span style="display: inline-block; position: relative; width: 1.602em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.55em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-267" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.041em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.47em;"><span class="texatom" id="MathJax-Span-268"><span class="mrow" id="MathJax-Span-269"><span class="mtext" id="MathJax-Span-270" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.539em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.426em; border-left: 0px solid; width: 0px; height: 1.288em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-35">P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}}</script></span> </h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
The relationship <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-271" style="width: 7.731em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.326em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1006.33em, 2.989em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-272"><span class="msubsup" id="MathJax-Span-273"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-274" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-275"><span class="mrow" id="MathJax-Span-276"><span class="mtext" id="MathJax-Span-277" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-278" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-279" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-280" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-281"><span class="mrow" id="MathJax-Span-282"><span class="mtext" id="MathJax-Span-283" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-284"><span style="display: inline-block; position: relative; width: 1.642em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-285" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-286"><span class="mrow" id="MathJax-Span-287"><span class="mtext" id="MathJax-Span-288" style="font-size: 70.7%; font-family: STIXGeneral;">rms</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>rms</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-36">P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}}</script></span> is an important equation when working with electric circuits.
</p>
</div>
<ol class="multi-part-entries"><li class="multi-part-entry">
<div class="problem">
<p>
What does the symbol <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-289" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-290"><span class="msubsup" id="MathJax-Span-291"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-292" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-293"><span class="mrow" id="MathJax-Span-294"><span class="mtext" id="MathJax-Span-295" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-37"> P_{\text{avg}}</script></span> represent?
</p>
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<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The symbol <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-296" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-297"><span class="msubsup" id="MathJax-Span-298"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-299" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-300"><span class="mrow" id="MathJax-Span-301"><span class="mtext" id="MathJax-Span-302" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-38">P_{\text{avg}}</script></span> represents the <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">minimum</option><option value="1">maximum</option><option value="2">root mean square</option><option value="3" selected="">average</option></select> <select name="question1b" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">momentum</option><option value="1">impedance</option><option value="2">current</option><option value="3" selected="">power</option><option value="4">potential difference</option></select>.
</p>
</div></div></div>
</li>
<li class="multi-part-entry">
<div class="problem">
<p>
What is the SI unit used to measure <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-303" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-304"><span class="msubsup" id="MathJax-Span-305"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-306" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-307"><span class="mrow" id="MathJax-Span-308"><span class="mtext" id="MathJax-Span-309" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-39">P_{\text{avg}}</script></span>?</span>
</p>
</div>
<div class="response"><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The SI unit used to measure <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-310" style="width: 2.111em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.7em, 2.638em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-311"><span class="msubsup" id="MathJax-Span-312"><span style="display: inline-block; position: relative; width: 1.701em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-313" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-314"><span class="mrow" id="MathJax-Span-315"><span class="mtext" id="MathJax-Span-316" style="font-size: 70.7%; font-family: STIXGeneral;">avg</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.425em; border-left: 0px solid; width: 0px; height: 1.289em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>avg</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-40">P_{\text{avg}}</script></span> is <select name="question2a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">C</option><option value="1">A</option><option value="2">V</option><option value="3">N</option><option value="4" selected="">W</option></select>.
</p>
</div></div></div>
</li>
</ol></div><input name="response_hash" type="hidden" value="2019-04-16T17:52:15.983126"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form></div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id3631-9160">ID is: 3631 Seed is: 9160<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">
The relationship between <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-317" style="width: 2.305em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.88em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-318"><span class="msubsup" id="MathJax-Span-319"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.71em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-320" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.119em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-321"><span class="mrow" id="MathJax-Span-322"><span class="mtext" id="MathJax-Span-323" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-41">P_{\text{max}}</script></span>,</span> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-324" style="width: 2.149em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.758em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.76em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-325"><span class="msubsup" id="MathJax-Span-326"><span style="display: inline-block; position: relative; width: 1.758em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.55em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-327" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.041em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.47em;"><span class="texatom" id="MathJax-Span-328"><span class="mrow" id="MathJax-Span-329"><span class="mtext" id="MathJax-Span-330" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-42">I_{\text{max}}</script></span>,</span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-331" style="width: 2.305em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.88em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-332"><span class="msubsup" id="MathJax-Span-333"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.74em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-334" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.197em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-335"><span class="mrow" id="MathJax-Span-336"><span class="mtext" id="MathJax-Span-337" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-43">V_{\text{max}}</script></span>
</h3>
</span><div class="problem">
<p>
Maximum power <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-338" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-339"><span class="mo" id="MathJax-Span-340" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-341"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-342" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-343"><span class="mrow" id="MathJax-Span-344"><span class="mtext" id="MathJax-Span-345" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-346" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-44">(P_{\text{max}})</script></span>,</span> maximum current <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-347" style="width: 2.93em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.403em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-348"><span class="mo" id="MathJax-Span-349" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-350"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-351" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-352"><span class="mrow" id="MathJax-Span-353"><span class="mtext" id="MathJax-Span-354" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-355" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-45">(I_{\text{max}})</script></span>,</span> and maximum potential difference <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-356" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-357"><span class="mo" id="MathJax-Span-358" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-359"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-360" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-361"><span class="mrow" id="MathJax-Span-362"><span class="mtext" id="MathJax-Span-363" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-364" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-46">(V_{\text{max}})</script></span> are three important quantities when working with alternating current (AC).
</p>
<p>
Which <strong>one</strong> of the following equations correctly represents the relationship between these quantities?
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-365" style="width: 8.317em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.794em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1006.79em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-366"><span class="msubsup" id="MathJax-Span-367"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-368" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-369"><span class="mrow" id="MathJax-Span-370"><span class="mtext" id="MathJax-Span-371" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-372" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-373" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-374" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-375"><span class="mrow" id="MathJax-Span-376"><span class="mtext" id="MathJax-Span-377" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-378"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-379" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-380"><span class="mrow" id="MathJax-Span-381"><span class="mtext" id="MathJax-Span-382" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-47">I_{\text{max}} = V_{\text{max}} P_{\text{max}}</script></span></td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-383" style="width: 6.443em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.272em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1005.27em, 3.516em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-384"><span class="msubsup" id="MathJax-Span-385"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-386" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-387"><span class="mrow" id="MathJax-Span-388"><span class="mtext" id="MathJax-Span-389" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-390" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mstyle" id="MathJax-Span-391" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-392"><span class="mfrac" id="MathJax-Span-393"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-394"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-395" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-396"><span class="mrow" id="MathJax-Span-397"><span class="mtext" id="MathJax-Span-398" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-399"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-400" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-401"><span class="mrow" id="MathJax-Span-402"><span class="mtext" id="MathJax-Span-403" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1001.99em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.994em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.068em; border-left: 0px solid; width: 0px; height: 2.789em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-48">I_{\text{max}} = \dfrac{P_{\text{max}}}{V_{\text{max}}}</script></span></td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-404" style="width: 6.443em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.272em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1005.27em, 3.516em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-405"><span class="msubsup" id="MathJax-Span-406"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-407" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-408"><span class="mrow" id="MathJax-Span-409"><span class="mtext" id="MathJax-Span-410" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-411" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mstyle" id="MathJax-Span-412" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-413"><span class="mfrac" id="MathJax-Span-414"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-415"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-416" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-417"><span class="mrow" id="MathJax-Span-418"><span class="mtext" id="MathJax-Span-419" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-420"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-421" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-422"><span class="mrow" id="MathJax-Span-423"><span class="mtext" id="MathJax-Span-424" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1001.99em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.994em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.068em; border-left: 0px solid; width: 0px; height: 2.789em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-49">I_{\text{max}} = \dfrac{V_{\text{max}}}{P_{\text{max}}}</script></span></td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The correct equation is: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1" selected="">B</option><option value="2">C</option></select>
</p>
</div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:15.999965"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id3631-126">ID is: 3631 Seed is: 126<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">
The relationship between <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-425" style="width: 2.305em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.88em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-426"><span class="msubsup" id="MathJax-Span-427"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.74em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-428" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.197em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-429"><span class="mrow" id="MathJax-Span-430"><span class="mtext" id="MathJax-Span-431" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-50">V_{\text{max}}</script></span>,</span> <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-432" style="width: 2.305em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.88em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-433"><span class="msubsup" id="MathJax-Span-434"><span style="display: inline-block; position: relative; width: 1.875em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.71em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-435" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.119em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.587em;"><span class="texatom" id="MathJax-Span-436"><span class="mrow" id="MathJax-Span-437"><span class="mtext" id="MathJax-Span-438" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-51">P_{\text{max}}</script></span>,</span> and <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-439" style="width: 2.149em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.758em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.407em, 1001.76em, 2.461em, -999.998em); top: -2.184em; left: 0em;"><span class="mrow" id="MathJax-Span-440"><span class="msubsup" id="MathJax-Span-441"><span style="display: inline-block; position: relative; width: 1.758em; height: 0px;"><span style="position: absolute; clip: rect(3.203em, 1000.55em, 4.1em, -999.998em); top: -3.979em; left: 0em;"><span class="mi" id="MathJax-Span-442" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.041em;"></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span><span style="position: absolute; top: -3.823em; left: 0.47em;"><span class="texatom" id="MathJax-Span-443"><span class="mrow" id="MathJax-Span-444"><span class="mtext" id="MathJax-Span-445" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.983em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.188em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.236em; border-left: 0px solid; width: 0px; height: 1.098em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-52">I_{\text{max}}</script></span>
</h3>
</span><div class="problem">
<p>
Maximum potential difference <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-446" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-447"><span class="mo" id="MathJax-Span-448" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-449"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-450" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-451"><span class="mrow" id="MathJax-Span-452"><span class="mtext" id="MathJax-Span-453" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-454" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-53">(V_{\text{max}})</script></span>,</span> maximum power <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-455" style="width: 3.106em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.52em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-456"><span class="mo" id="MathJax-Span-457" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-458"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-459" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-460"><span class="mrow" id="MathJax-Span-461"><span class="mtext" id="MathJax-Span-462" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-463" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-54">(P_{\text{max}})</script></span>,</span> and maximum current <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-464" style="width: 2.93em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.403em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.35em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-465"><span class="mo" id="MathJax-Span-466" style="font-family: STIXGeneral;">(</span><span class="msubsup" id="MathJax-Span-467"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-468" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-469"><span class="mrow" id="MathJax-Span-470"><span class="mtext" id="MathJax-Span-471" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-472" style="font-family: STIXGeneral;">)</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-55">(I_{\text{max}})</script></span> are three important quantities when working with alternating current (AC).
</p>
<p>
Which <strong>one</strong> of the following equations correctly represents the relationship between these quantities?
</p>
<table border="1"> <tbody><tr> <td style="background:lightgray"><strong>A</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-473" style="width: 8.317em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.794em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1006.79em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-474"><span class="msubsup" id="MathJax-Span-475"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-476" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-477"><span class="mrow" id="MathJax-Span-478"><span class="mtext" id="MathJax-Span-479" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-480" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="msubsup" id="MathJax-Span-481" style="padding-left: 0.296em;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-482" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-483"><span class="mrow" id="MathJax-Span-484"><span class="mtext" id="MathJax-Span-485" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="msubsup" id="MathJax-Span-486"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-487" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-488"><span class="mrow" id="MathJax-Span-489"><span class="mtext" id="MathJax-Span-490" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-56">V_{\text{max}} = I_{\text{max}} P_{\text{max}}</script></span></td></tr><tr> <td style="background:lightgray"><strong>B</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-491" style="width: 6.619em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.389em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1005.39em, 3.516em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-492"><span class="msubsup" id="MathJax-Span-493"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-494" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-495"><span class="mrow" id="MathJax-Span-496"><span class="mtext" id="MathJax-Span-497" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-498" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mstyle" id="MathJax-Span-499" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-500"><span class="mfrac" id="MathJax-Span-501"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.165em, 1001.76em, 4.335em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.875em;"><span class="msubsup" id="MathJax-Span-502"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-503" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-504"><span class="mrow" id="MathJax-Span-505"><span class="mtext" id="MathJax-Span-506" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-507"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-508" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-509"><span class="mrow" id="MathJax-Span-510"><span class="mtext" id="MathJax-Span-511" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1001.99em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.994em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.068em; border-left: 0px solid; width: 0px; height: 2.789em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-57">V_{\text{max}} = \dfrac{I_{\text{max}}}{P_{\text{max}}}</script></span></td></tr><tr> <td style="background:lightgray"><strong>C</strong></td> <td><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-512" style="width: 6.619em; display: inline-block;"><span style="display: inline-block; position: relative; width: 5.389em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(0.998em, 1005.39em, 3.516em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-513"><span class="msubsup" id="MathJax-Span-514"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-515" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-516"><span class="mrow" id="MathJax-Span-517"><span class="mtext" id="MathJax-Span-518" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-519" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mstyle" id="MathJax-Span-520" style="padding-left: 0.296em;"><span class="mrow" id="MathJax-Span-521"><span class="mfrac" id="MathJax-Span-522"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(3.165em, 1001.88em, 4.335em, -999.997em); top: -4.681em; left: 50%; margin-left: -0.934em;"><span class="msubsup" id="MathJax-Span-523"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.71em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-524" style="font-family: STIXGeneral; font-style: italic;">𝑃<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.12em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-525"><span class="mrow" id="MathJax-Span-526"><span class="mtext" id="MathJax-Span-527" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(3.165em, 1001.76em, 4.335em, -999.997em); top: -3.276em; left: 50%; margin-left: -0.875em;"><span class="msubsup" id="MathJax-Span-528"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.53em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-529" style="font-family: STIXGeneral; font-style: italic;">𝐼<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.061em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.471em;"><span class="texatom" id="MathJax-Span-530"><span class="mrow" id="MathJax-Span-531"><span class="mtext" id="MathJax-Span-532" style="font-size: 70.7%; font-family: STIXGeneral;">max</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; clip: rect(0.823em, 1001.99em, 1.232em, -999.997em); top: -1.285em; left: 0em;"><span style="display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 1.994em; height: 0px;"></span><span style="display: inline-block; width: 0px; height: 1.057em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.068em; border-left: 0px solid; width: 0px; height: 2.789em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><msub><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub><msub><mi>I</mi><mrow class="MJX-TeXAtom-ORD"><mtext>max</mtext></mrow></msub></mfrac></mstyle></math></span></span><script type="math/tex" id="MathJax-Element-58">V_{\text{max}} = \dfrac{P_{\text{max}}}{I_{\text{max}}}</script></span></td></tr></tbody></table>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The correct equation is: <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">A</option><option value="1">B</option><option value="2" selected="">C</option></select>
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<span class="worked_example"><h3 class="sv-heading">Energy-efficiency of a tumble dryer</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from WCED Metro Central Sep 2017 Grade 12, P1, Q9.2</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The energy-efficiency of a tumble dryer can be defined as a measure of the amount of energy it uses per unit time in order to produce a given heating effect.
</p>
<p>
A manufacturer claims that their tumble dryer is more energy-efficient than older tumble dryers. To test these claims, some researchers connect the tumble dryer to an AC generator which produces a root mean square voltage of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>200</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-533" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-534"><span class="mtext" id="MathJax-Span-535" style="font-family: STIXGeneral;">200</span><span class="mtext" id="MathJax-Span-536" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-537" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>200</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-59">\text{200}\ \text{V}</script></span>. The researchers manage to produce the same heating effect as the manufacturer. They measure the current passing through the tumble dryer over time and plot the following graph:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4040/9882/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(10)"></a></div>
<p>
The following information was taken from a label on the back of the tumble dryer:
</p>
<div class="quote">
<p class="centre">
<strong>RATING:</strong> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>200</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-538" style="width: 3.047em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.462em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-539"><span class="mtext" id="MathJax-Span-540" style="font-family: STIXGeneral;">200</span><span class="mtext" id="MathJax-Span-541" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-542" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>200</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-60">\text{200}\ \text{V}</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x223C;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-543" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.994em, 1000.65em, 2.52em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-544"><span class="mo" id="MathJax-Span-545" style="font-family: STIXGeneral;">∼</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.146em; border-left: 0px solid; width: 0px; height: 0.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∼</mo></math></span></span><script type="math/tex" id="MathJax-Element-61">\sim</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>70</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-546" style="width: 2.93em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.403em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.4em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-547"><span class="mtext" id="MathJax-Span-548" style="font-family: STIXGeneral;">70</span><span class="mtext" id="MathJax-Span-549" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-550" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>70</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-62">\text{70}\ \text{Hz}</script></span>, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1&#xA0;400</mtext><mtext>&#xA0;</mtext><mtext>W</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-551" style="width: 4.218em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.457em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-552"><span class="mtext" id="MathJax-Span-553" style="font-family: STIXGeneral;">1 400</span><span class="mtext" id="MathJax-Span-554" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-555" style="font-family: STIXGeneral;">W</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1 400</mtext><mtext> </mtext><mtext>W</mtext></math></span></span><script type="math/tex" id="MathJax-Element-63">\text{1 400}\ \text{W}</script></span>
</p>
</div>
<p>
Is the tumble dryer as energy-efficient as the manufacturer claims? Perform a calculation to support your answer.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The measured <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">current draw</option><option value="1">resistance</option><option value="2">voltage</option><option value="3" selected="">power</option></select> is <input name="question1b" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1 305,32" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>W</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-556" style="width: 1.174em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.94em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.94em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-557"><span class="mtext" id="MathJax-Span-558" style="font-family: STIXGeneral;">W</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>W</mtext></math></span></span><script type="math/tex" id="MathJax-Element-64">\text{W}</script></span>.<br>
This is <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">greater than</option><option value="1">almost equal to</option><option value="2" selected="">less than</option></select> the claimed value. <br>
So the tumble dryer is <select name="question1d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">more efficient than</option><option value="1">as efficient as</option><option value="2">less efficient than</option></select> claimed.
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:16.061259"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><section class="sv-section sv-question sv-table"><br><div class="id4040-9250">ID is: 4040 Seed is: 9250<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Energy-efficiency of a water heater</h3>
</span><div class="problem">
<p>
<span class="colored" style="color:gray"><em>Adapted from WCED Metro Central Sep 2017 Grade 12, P1, Q9.2</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The energy-efficiency of a water heater can be defined as a measure of the amount of energy it uses per unit time in order to produce a given heating effect.
</p>
<p>
A manufacturer claims that their water heater is more energy-efficient than older water heaters. To test these claims, some researchers connect the water heater to an AC generator which produces a root mean square current of <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mtext>&#xA0;</mtext><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-559" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-560"><span class="mtext" id="MathJax-Span-561" style="font-family: STIXGeneral;">15</span><span class="mtext" id="MathJax-Span-562" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-563" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mtext> </mtext><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-65">\text{15}\ \text{A}</script></span>. The researchers manage to produce the same heating effect as the manufacturer. They measure the potential difference across the water heater over time and plot the following graph:
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/4040/9250/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(11)"></a></div>
<p>
The following information was taken from a label on the back of the water heater:
</p>
<div class="quote">
<p class="centre">
<strong>RATING:</strong> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mtext>&#xA0;</mtext><mtext>A</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-564" style="width: 2.462em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.994em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1001.99em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-565"><span class="mtext" id="MathJax-Span-566" style="font-family: STIXGeneral;">15</span><span class="mtext" id="MathJax-Span-567" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-568" style="font-family: STIXGeneral;">A</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>15</mtext><mtext> </mtext><mtext>A</mtext></math></span></span><script type="math/tex" id="MathJax-Element-66">\text{15}\ \text{A}</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&#x223C;</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-569" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.994em, 1000.65em, 2.52em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-570"><span class="mo" id="MathJax-Span-571" style="font-family: STIXGeneral;">∼</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: 0.146em; border-left: 0px solid; width: 0px; height: 0.432em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∼</mo></math></span></span><script type="math/tex" id="MathJax-Element-67">\sim</script></span> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>55</mtext><mtext>&#xA0;</mtext><mtext>Hz</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-572" style="width: 2.93em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.403em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1002.4em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-573"><span class="mtext" id="MathJax-Span-574" style="font-family: STIXGeneral;">55</span><span class="mtext" id="MathJax-Span-575" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-576" style="font-family: STIXGeneral;">Hz</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>55</mtext><mtext> </mtext><mtext>Hz</mtext></math></span></span><script type="math/tex" id="MathJax-Element-68">\text{55}\ \text{Hz}</script></span>, <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1&#xA0;400</mtext><mtext>&#xA0;</mtext><mtext>W</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-577" style="width: 4.218em; display: inline-block;"><span style="display: inline-block; position: relative; width: 3.457em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1003.46em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-578"><span class="mtext" id="MathJax-Span-579" style="font-family: STIXGeneral;">1 400</span><span class="mtext" id="MathJax-Span-580" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-581" style="font-family: STIXGeneral;">W</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>1 400</mtext><mtext> </mtext><mtext>W</mtext></math></span></span><script type="math/tex" id="MathJax-Element-69">\text{1 400}\ \text{W}</script></span>
</p>
</div>
<p>
Is the water heater as energy-efficient as the manufacturer claims? Perform a calculation to support your answer.
</p>
<div class="note instruction"><span class="note-header">INSTRUCTION:</span>
Round your answer to <strong>two decimal places</strong>.
</div>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span>
<p>
The measured <select name="question1a" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">voltage</option><option value="1">current draw</option><option value="2" selected="">power</option><option value="3">resistance</option></select> is <input name="question1b" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="1 672,24" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>W</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-582" style="width: 1.174em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.94em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.94em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-583"><span class="mtext" id="MathJax-Span-584" style="font-family: STIXGeneral;">W</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>W</mtext></math></span></span><script type="math/tex" id="MathJax-Element-70">\text{W}</script></span>.<br>
This is <select name="question1c" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0" selected="">greater than</option><option value="1">almost equal to</option><option value="2">less than</option></select> the claimed value. <br>
So the water heater is <select name="question1d" class="response-query-input" autocomplete="off"><option value="">Select</option><option value="0">more efficient than</option><option value="1">as efficient as</option><option value="2" selected="">less efficient than</option></select> claimed.
</p>
<div class="response-type">one-of<div class="response-subtype">type(numeric.abserror(0.01))</div></div></div></div></div>
<input name="response_hash" type="hidden" value="2019-04-16T17:52:16.103502"><div class="sv"><div class="sv-form__actions" id="nav-buttons"></div></div></form>
</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id2329-4500">ID is: 2329 Seed is: 4500<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Electrodynamic properties of appliances: root mean square voltage</h3>
</span><div class="problem">
<p>
A scientist is investigating the electrodynamic properties of a microwave oven.
</p>
<p>
The figure on the right shows a simplified circuit diagram of the microwave oven.
</p>
<p>
</p><div class="figure"><a href="https://www.emas.com/practice/isolated_image/2329/4500/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(12)"></a></div>
<p></p>
<p>
The scientist has measured the maximum voltage of the alternating current supplied to the microwave oven as <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mtext>235,77</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-585" style="width: 8.375em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.853em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1006.85em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-586"><span class="msubsup" id="MathJax-Span-587"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-588" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-589"><span class="mrow" id="MathJax-Span-590"><span class="mi" id="MathJax-Span-591" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-592" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-593" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-594" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-595" style="font-family: STIXGeneral; padding-left: 0.296em;">235,77</span><span class="mtext" id="MathJax-Span-596" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-597" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mtext>235,77</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-71">V_{max} = \text{235,77}\ \text{V}</script></span>.</span>
</p>
<p>
What is the <strong>root mean square voltage</strong> of the alternating current supplied to the microwave oven, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-598" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.76em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-599"><span class="msubsup" id="MathJax-Span-600"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-601" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-602"><span class="mrow" id="MathJax-Span-603"><span class="mi" id="MathJax-Span-604" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-605" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-606" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-72">V_{rms}</script></span>?</span>
</p>
<ul>
<li>round your answer to <strong>two decimal places</strong></li>
<li>use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a></li>
</ul>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-607" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.7em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-608"><span class="msubsup" id="MathJax-Span-609"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-610" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-611"><span class="mrow" id="MathJax-Span-612"><span class="mi" id="MathJax-Span-613" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-614" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-615" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-616" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-73">V_{rms} = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="166,71" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-617" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-618"><span class="mtext" id="MathJax-Span-619" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-74">\text{V}</script></span><div class="response-type">numeric</div></div></div></div>
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</div></section><section class="sv-section sv-question sv-table"><br><div class="id2329-1457">ID is: 2329 Seed is: 1457<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST">
<span class="worked_example"><h3 class="sv-heading">Electrodynamic properties of appliances: root mean square voltage</h3>
</span><div class="problem">
<p>
A designer is investigating the electrodynamic properties of a handheld blender.
</p>
<p>
The figure on the right shows a simplified circuit diagram of the handheld blender.
</p>
<p>
</p><div class="figure"><a href="https://www.emas.com/practice/isolated_image/2329/1457/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(13)"></a></div>
<p></p>
<p>
The designer has measured the maximum voltage of the alternating current supplied to the handheld blender as <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mtext>220,16</mtext><mtext>&#xA0;</mtext><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-620" style="width: 8.375em; display: inline-block;"><span style="display: inline-block; position: relative; width: 6.853em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.642em, 1006.85em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-621"><span class="msubsup" id="MathJax-Span-622"><span style="display: inline-block; position: relative; width: 1.876em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-623" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-624"><span class="mrow" id="MathJax-Span-625"><span class="mi" id="MathJax-Span-626" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-627" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑎</span><span class="mi" id="MathJax-Span-628" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑥</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-629" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span><span class="mtext" id="MathJax-Span-630" style="font-family: STIXGeneral; padding-left: 0.296em;">220,16</span><span class="mtext" id="MathJax-Span-631" style="font-family: STIXGeneral;"> </span><span class="mtext" id="MathJax-Span-632" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><mtext>220,16</mtext><mtext> </mtext><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-75">V_{max} = \text{220,16}\ \text{V}</script></span>.</span>
</p>
<p>
What is the <strong>root mean square voltage</strong> of the alternating current supplied to the handheld blender, or <span class="latex-math-wrapper"><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-633" style="width: 2.169em; display: inline-block;"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.35em, 1001.76em, 2.52em, -999.997em); top: -2.163em; left: 0em;"><span class="mrow" id="MathJax-Span-634"><span class="msubsup" id="MathJax-Span-635"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-636" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-637"><span class="mrow" id="MathJax-Span-638"><span class="mi" id="MathJax-Span-639" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-640" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-641" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.169em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-76">V_{rms}</script></span>?</span>
</p>
<ul>
<li>round your answer to <strong>two decimal places</strong></li>
<li>use the values for any physical constants you might need, as listed <a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">here</a></li>
</ul>
</div>
<div class="response"><a name="next-response"> </a><div class="response-query"><div class="response-query-body"><span class="emphasis-bold answer">Answer:</span><span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-642" style="width: 3.399em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1002.7em, 2.872em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-643"><span class="msubsup" id="MathJax-Span-644"><span style="display: inline-block; position: relative; width: 1.759em; height: 0px;"><span style="position: absolute; clip: rect(3.165em, 1000.76em, 4.16em, -999.997em); top: -3.978em; left: 0em;"><span class="mi" id="MathJax-Span-645" style="font-family: STIXGeneral; font-style: italic;">𝑉<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.179em;"></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span><span style="position: absolute; top: -3.803em; left: 0.588em;"><span class="texatom" id="MathJax-Span-646"><span class="mrow" id="MathJax-Span-647"><span class="mi" id="MathJax-Span-648" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑟</span><span class="mi" id="MathJax-Span-649" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑚</span><span class="mi" id="MathJax-Span-650" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">𝑠</span></span></span><span style="display: inline-block; width: 0px; height: 3.984em;"></span></span></span></span><span class="mo" id="MathJax-Span-651" style="font-family: STIXGeneral; padding-left: 0.296em;">=</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.146em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow class="MJX-TeXAtom-ORD"><mi>r</mi><mi>m</mi><mi>s</mi></mrow></msub><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-77">V_{rms} = </script></span> <input name="question1a" class="response-query-input" type="text" autocapitalize="none" autocomplete="off" autocorrect="off" spellcheck="false" value="155,68" size="10"> <span class="latex-math"><span class="MathJax_Preview" style="color: inherit;"></span><span class="MathJax" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-652" style="width: 0.881em; display: inline-block;"><span style="display: inline-block; position: relative; width: 0.706em; height: 0px; font-size: 122%;"><span style="position: absolute; clip: rect(1.701em, 1000.71em, 2.696em, -999.997em); top: -2.515em; left: 0em;"><span class="mrow" id="MathJax-Span-653"><span class="mtext" id="MathJax-Span-654" style="font-family: STIXGeneral;">V</span></span><span style="display: inline-block; width: 0px; height: 2.52em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 0.932em;"></span></span></nobr><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>V</mtext></math></span></span><script type="math/tex" id="MathJax-Element-78">\text{V}</script></span><div class="response-type">numeric</div></div></div></div>
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</div></section><hr><section class="sv-section sv-question sv-table"><br><div class="id3848-1263">ID is: 3848 Seed is: 1263<br><form name="questions" action="https://www.emas.com/sandbox/nigeria-chapter/f950fa80-282d-5663-8352-8ef9884db613" method="POST"><span class="worked_example"><h3 class="sv-heading">Generators</h3>
</span><div class="multi-part"><div class="multi-part-header">
<p>
<span class="colored" style="color:gray"><em>Adapted from DBE Feb-Mar 2017 Grade 12, P1, Q9</em></span> <br>
<a url="/info/physical-constants" href="https://www.emas.com/info/physical-constants">Physical constants</a> · <a url="/info/physics-formulas" href="https://www.emas.com/info/physics-formulas">Physics formulas</a>
</p>
<p>
The diagram below shows a simplified version of a DC generator.
</p>
<div class="figure"><a href="https://www.emas.com/practice/isolated_image/3848/1263/0"><img src="./CAPS-Science-Grade-12-11-Electrodynamics_files/0(14)"></a></div>
</div>