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14px"><i class="fa fa-fw"></i><a href="../1136/capacitors.html">Capacitors</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Transformers <a href="#" class="mark-page-favorite pull-right" data-pid="1140" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../445/electricity-and-magnetism.html">Electricity and magnetism</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1144/ahl-em-induction.html">AHL EM induction</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Transformers</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../em-induction/power-lines.jpg" style="float: left; width: 250px; height: 166px;">AC generators in power stations use electromagnetic induction to convert kinetic into electrical energy. Electromagnetic induction is then used in transformers to transmit the electricity efficiently to where it is needed.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Operation</p> </div> </div> <div class="panel-body"> <div> <p>A transformer consists of two coils - primary and secondary. The primary coil produces a changing magnetic field due to the alternating current supplied within. The secondary coil cuts the changing magnetic flux and a changing EMF is induced, causing a current to flow. The strength of the magnetic field is increased by the presence of the solf iron core.</p> <p style="text-align: center;"><img alt="" src="../../em-induction/transformer3d_col3.svg" style="width: 500px; height: 375px;"></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369634636"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Equation</p> </div> </div> <div class="panel-body"> <div> <p>A step-up transformer increases the EMF and has more turns on the secondary coil in comparison with the primary. A step-down transformer decreases EMF and has a reduction in the number of turns.</p> <p>In both cases, the ratio of the EMFs is equal to the ratio of the turns:</p> <p style="text-align: center;"><span class="math-tex">\({\varepsilon_p\over \varepsilon_s}={N_p\over N_s}\)</span></p> <p>If the transformer is ideal, the power input is equal to the power output:</p> <p style="text-align: center;"><span class="math-tex">\(I_p\varepsilon_p=I_s\varepsilon_s\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow {\varepsilon_p\over \varepsilon_s}={N_p\over N_s}={I_s\over I_p}\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon_p\)</span> is the EMF on the primary coil (V)</li> <li><span class="math-tex">\(\varepsilon_s\)</span> is the EMF on the secondary coil (V)</li> <li><span class="math-tex">\(N_p\)</span> is the number of turns on the primary coil</li> <li><span class="math-tex">\(N_s\)</span> is the number of turns on the secondary coil</li> <li><span class="math-tex">\(I_s\)</span> is the current in the secondary coil (A)</li> <li><span class="math-tex">\(I_p\)</span> is the current in the primary coil (A)</li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369634695"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-yellow panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Power transmission</p> </div> </div> <div class="panel-body"> <div> <p>The process of transmitting electrical power from a generator to a town is optimised to reduce thermal energy losses.</p> <p>The main culprit is usually thermal energy loss in power lines, due to the size of the current. To reduce this current and hence the wasted energy:</p> <ol> <li>A step-up transformer is used before the power lines (to increase voltage an reduce current)</li> <li>A step-down transformer is used after the power lines (to reduce voltage to an acceptable size for household use)</li> </ol> <p style="text-align: center;"><iframe height="566px" scrolling="no" src="https://tube.geogebra.org/material/iframe/id/1357705/width/453/height/566/border/888888/rc/false/ai/false/sdz/false/smb/false/stb/false/stbh/true/ld/false/sri/true/at/auto" style="border:0px;" width="453px"></iframe></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/369634721"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Non-ideal transformers</p> </div> </div> <div class="panel-body"> <div> <p>There are several reasons why transformers are not ideal:</p> <ul> <li>Flux leakage - some of the flux does not travel through the soft iron core but instead through the air. This is not cut by the secondary coil.</li> <li>Joule heating - the currents in the coils will experience resistance and release thermal energy</li> <li>Eddy current heating - the soft iron core will be subject to the induction of loops of current perpendicular to the field. These will release thermal energy.</li> <li>Magnetic hysteresis - when a magnetic field is applied to the soft iron core, the atomic domains align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. This alignment requires work to be overcome as the field direction changes continuously.</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#c3111ca1"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="c3111ca1"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> The AC generator and transformer <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-351-1140" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A straight conductor of length <span class="math-tex">\(x\)</span> travels through a perpendicular magnetic field of flux density <span class="math-tex">\(y\)</span> with constant speed <span class="math-tex">\(z\)</span>.</p><p>The induced EMF between the ends of the conductor is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(xyz\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(yz\over x\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(y\over xz\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(xy\over z\)</span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(\varepsilon = BLv =yxz\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>An AC generator induces 12 V at 100 revolutions per second.</p><p>The freqency is increased to 200 revolutions per second. What are the new output voltage and time period?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>12 V, 10 ms</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>24 V, 5 ms</span></label> </p><p><label class="radio"> <input type="radio"> <span>24 V, 50 ms</span></label> </p><p><label class="radio"> <input type="radio"> <span>12 V, 5 ms</span></label> </p></div><div class="q-explanation"><p>The initial time period is <span class="math-tex">\({1\over 100}=0.01 \text{ s}=10\text { ms}\)</span></p><p>Doubling the frequency doubles the induced EMF and halves the time period.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates in a uniform field <span class="math-tex">\(B\)</span>.</p><p style="text-align: center;"><img alt="" height="201" src="../../screenshot-2019-09-25-at-17.58.55.png" width="235"></p><p>When the induced EMF is maximum, the flux enclosed is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(BA\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(B\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(BAN\)</span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(0\)</span></span></label> </p></div><div class="q-explanation"><p>The EMF, which is proportional to the rate of change of flux, is greatest when flux enclosed is zero. This is because there is the largest possible change in flux.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates in a uniform field <span class="math-tex">\(B\)</span>.</p><p style="text-align: center;"><img alt="" height="201" src="../../screenshot-2019-09-25-at-17.58.55.png" width="235"></p><p>When the induced EMF is zero, the flux linkage is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(B\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(0\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(BA\)</span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(BAN\)</span></span></label> </p></div><div class="q-explanation"><p>Rate of change of flux is minimum when the flux enclosed is maximum.</p><p><span class="math-tex">\(N\Phi=BAN\cos \theta\)</span> is maximised when <span class="math-tex">\(\cos \theta=1\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates clockwise in a uniform field <span class="math-tex">\(B\)</span>.</p><p style="text-align: center;"><img alt="" height="201" src="../../screenshot-2019-09-25-at-17.58.55.png" width="235"></p><p>At the position shown the EMF is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>increasing from a minimum</span></label> </p><p><label class="radio"> <input type="radio"> <span>decreasing from a maximum</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>increasing from zero</span></label> </p><p><label class="radio"> <input type="radio"> <span>zero</span></label> </p></div><div class="q-explanation"><p>The clockwise rotation means that the top and bottom of the coil were recently moving parallel to the field lines when no EMF was induced.</p><p>The EMF could now be increasing or decreasing (but will be increasing in magnitude) depending on which direction is taken to be positive.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates in a uniform field <span class="math-tex">\(B\)</span>.</p><p style="text-align: center;"><img alt="" src="../../rotcoil4.png" style="width: 237px; height: 193px;"></p><p>At what angle <span class="math-tex">\(\theta\)</span> will the EMF be half its maximum value?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>60°</span></label> </p><p><label class="radio"> <input type="radio"> <span>90°</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>30°</span></label> </p><p><label class="radio"> <input type="radio"> <span>45°</span></label> </p></div><div class="q-explanation"><p>The EMF induced is proportional to <span class="scayt-misspell-word" data-scayt-word="sinθ" data-wsc-lang="en_US"><span class="math-tex">\(\sin\theta\)</span>. When <span class="math-tex">\(\sin \theta={1\over 2}\)</span>, <span class="math-tex">\(\theta = 30°\)</span>.</span></p><p>NB: We can check that <span class="math-tex">\(\sin\theta\)</span> is appropriate here by noticing that the angle is between the perpendicular and the field lines.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates in a magnetic field <span class="math-tex">\(B\)</span> with frequency <span class="math-tex">\(f\)</span>. The mean value of the induced EMF is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BANπf" data-wsc-lang="en_US"></span></span></label><span class="math-tex">\(BAN\sqrt2πf\)</span> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(0\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BAN2πf" data-wsc-lang="en_US"><span class="math-tex">\(BAN2πf\)</span></span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BANπf" data-wsc-lang="en_US"><span class="math-tex">\(BANπf\)</span></span></span></label> </p></div><div class="q-explanation"><p>Note that the average requested was the 'mean'. Since EMF is sinusoidal (<span class="math-tex">\(\varepsilon = BANω\sinθ\)</span><span class="scayt-misspell-word" data-scayt-word="BANωsinθ" data-wsc-lang="en_US">), the mean is 0.</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A coil with <span class="math-tex">\(N\)</span> turns and area <span class="math-tex">\(A\)</span> rotates in a magnetic field <span class="math-tex">\(B\)</span> with frequency <span class="math-tex">\(f\)</span>. The rms value of the induced EMF is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BAN2πf" data-wsc-lang="en_US"><span class="math-tex">\(BAN2πf\)</span></span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BANπf" data-wsc-lang="en_US"></span></span></label><span class="math-tex">\(BANπf\over \sqrt2\)</span> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BANπf" data-wsc-lang="en_US"></span></span></label><span class="math-tex">\(BAN\sqrt2πf\)</span> </p><p><label class="radio"> <input type="radio"> <span><span class="scayt-misspell-word" data-scayt-word="BANπf" data-wsc-lang="en_US"><span class="math-tex">\(BANπf\)</span></span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(\varepsilon_\text{rms} = {\varepsilon_0\over \sqrt2} ={BAN2πf\over \sqrt2}=BAN\sqrt2 \pi f\)</span><span class="scayt-misspell-word" data-scayt-word="BAN2πfsinθ" data-wsc-lang="en_US"></span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Light bulb A is connected to an AC supply of peak voltage 6 V. An identical bulb B is connected to a 6 V battery.</p><p>What is the ratio <span class="math-tex">\(\text{power dissipated in A} \over \text{power dissipated in B}\)</span>?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over\sqrt2\)</span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(1\over2\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt2\)</span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(P_\text{A}={{V_\text{rms}}^2\over R} ={{V_0}^2\over {\sqrt2}^2R}={1\over 2}{{V_0}^2\over R}={1\over2}P_\text{B}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Light bulb A is connected to an AC supply of rms voltage 6 V. An identical bulb B is connected to a 6 V battery.</p><p>What is the ratio <span class="math-tex">\(\text{power dissipated in A} \over \text{power dissipated in B}\)</span>?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt2\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over\sqrt2\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 2\)</span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(1\)</span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(P_\text{A}={{V_\text{rms}}^2\over R}=P_\text{B}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Identical components are connected in two different ways to produce two different transformers, A and B.</p><p style="text-align: center;"><img alt="" height="173" src="../../screenshot-2019-09-26-at-07.18.29.png" width="291"></p><p>What is the ratio <span class="math-tex">\(V_\text{rms} \text{ across load A} \over V_\text{rms} \text{ across load B}\)</span>?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(1\over4\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt2\over 4\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(4\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(4\over\sqrt2\)</span></span></label> </p></div><div class="q-explanation"><p>Let's call the EMF of the supply <span class="math-tex">\(\varepsilon\)</span>:</p><p><span class="math-tex">\(V_\text{load A}={\varepsilon\over 2}\)</span></p><p><span class="math-tex">\(V_\text{load B}=2{\varepsilon}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The rms voltage of the supply in the diagram is 6 V and the load resistor has resistance 1 kΩ.</p><p style="text-align: center;"><img alt="" height="164" src="../../screenshot-2019-09-26-at-12.53.09.png" width="159"></p><p>The peak current through the load is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(24\text{ mA}\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(12\text{ mA}\)</span></span></label> </p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\({12\over \sqrt2}\text{ mA}\)</span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(\sqrt2 \times 12\text{ mA}\)</span></span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(N_s/N_p = 2\Rightarrow V_\text{rms}=12 \text{ V}\)</span></p><p><span class="math-tex">\(I_\text{rms} = {12\over1000} = 12 \text{ mA}\)</span></p><p><span class="math-tex">\(I_0=\sqrt2 I_\text{rms}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A power station delivers 2 MW at a potential difference of 50 kV through cables of resistance 4 Ω.</p><p style="text-align: center;"><img alt="" height="169" src="../../screenshot-2019-09-26-at-13.12.46.png" width="324"></p><p>The <span class="scayt-misspell-word" data-scayt-word="curreent" data-wsc-lang="en_US">current</span> through the cables is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>12.5 kA</span></label> </p><p><label class="radio" style=" float: left; margin-right: 40px; "> <input class="c" type="radio"> <span>40 A</span></label> </p><p><label class="radio" style=" float: left; margin-right: 40px; "> <input type="radio"> <span>400 A</span></label> </p><p><label class="radio" style=" float: left; margin-right: 40px; "> <input type="radio"> <span>12.5 A</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(P=IV \Rightarrow I={P\over V}={2\times 10^6\over 50\times 10^3}=40\text{ A}\)</span></p><p>NB: We cannot use <span class="math-tex">\(V = IR\)</span> as the potential difference given is across the power station (and not across the cables).</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa 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