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href="../181/electric-circuits.html">Electric circuits</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Parallel resistors</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="../../electricity/13-parallel-sm.jpg" style="float: left; width: 250px; height: 141px;">Not every circuit contains both parallel and series sections, but the ones in your exam probably will. Start with short sections that are clearly just series <strong>or</strong> parallel and merge these resistors together. Then, when the diagram is simplified, you will be able to combine the new resistors. </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> <p>Combining resistors in parallel is slightly more complicated than in series:</p> <ul> <li>Resistors in parallel have the same potential difference across them. This is a result of Kirchhoff's second law, as the potential difference in any complete loop of the circuit must equal the EMF.</li> <li>However, current splits at a parallel junction in inverse ratio to the resistance.</li> <li>The resistance of a parallel combination is less than the individual resistors.</li> </ul> <p>The equation is <span class="math-tex">\({1\over R_T}={1\over R_1}+{1\over R_2}+...\)</span></p> <p>NB: Think the algebra looks simple? Think again. You will need to combine the total right hand side before you flip.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <h4 style="text-align: center;"><span class="math-tex">\({1\over R_T}={R_2\over R_1R_2}+{R_1\over R_1R_2}\)</span></h4> <h4 style="text-align: center;"><span class="math-tex">\({1\over R_T}={R_1+R_2\over R_1R_2}\)</span></h4> <h4 style="text-align: center;"><span class="math-tex">\({R_T}={R_1R_2 \over R_1+R_2 }\)</span></h4> <p>The equation becomes easier with equal resistances - with two, you can simply half either resistance (and with three, take a third, etc).</p> </section> <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/158796871"></iframe></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-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Potential difference across parallel resistors</p> </div> </div> <div class="panel-body"> <div> <p>When dealing with resistor networks calculate the resistance of the parallel bits first.</p> <p>In which order should you approach the following circuit?</p> <p style="text-align: center;"><img alt="" src="../../electricity/circuit-_1_.png" style="width: 400px; height: 246px;"></p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <ul> <li>Combine series section R1 and R2</li> <li>Combine series section R3 and R4</li> <li>These will then become a parallel section - combine this</li> <li>Combine your new resistor (containing R1, R2, R3 and R4) with R5 and R6</li> <li>You then have one overall resistor in parallel with R7</li> </ul> </section> <p style="text-align: center;"> <iframe allowfullscreen="" frameborder="0" height="368" mozallowfullscreen="" src="https://player.vimeo.com/video/159667123" webkitallowfullscreen="" width="500"></iframe></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>What about light bulb filaments?</p> </div> </div> <div class="panel-body"> <div> <p>So far we have considered only simple resistors that produce thermal energy. If these resistors are replaced with identical light bulb filaments, that with the largest current will be brightest.</p> <p>There are a couple of advantages to connecting several light bulbs in parallel, rather than in series:</p> <ul> <li>A broken bulb can quickly be identified as it will be the only one to go out (and they can be switched on and off independently)</li> <li>The bulbs will be brighter than the equivalent series combination as each has a direct connection to the EMF (NB: the circuit will use more electrical power, however) </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/159668975"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div 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src="../../images/bulbsq1.png" style="width: 394px; height: 226px;"></p><p>Which bulb doesn't light when switch 1 is closed?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>A is short circuited no current will pass through it.</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 diagram shows 4 bulbs a battery and 2 switches</p><p style="text-align: center;"><img alt="" src="../../images/bulbsq1.png" style="width: 394px; height: 226px;"></p><p>Which bulb is brightest when switch 1 is closed?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p></div><div class="q-explanation"><p>Twice as much current passes through B than D and C</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 diagram shows 4 bulbs a battery and 2 switches</p><p style="text-align: center;"><img alt="" src="../../images/bulbsq1.png" style="width: 394px; height: 226px;"></p><p>If switch 1 is closed then switch 2 opened what will happen to the lights?</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> A will light BC and D will get dimmer</label></p><p><label class="radio"><input type="radio"> A will light B and C get brighter but D gets dimmer</label></p><p><label class="radio"><input type="radio"> A will light BC and D will get brighter</label></p><p><label class="radio"><input type="radio"> A will light B and C get dimmer but D gets brighter</label></p></div><div class="q-explanation"><p>A is no longer short circuited so the resistance of the circuit increases all 3 bulbs get dimmer.</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/images/bulbsq3.gif" style="width: 408px; height: 232px;"></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i 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</div> </div> <div class="panel-body"> <div><em>Online tutorials to help you solve original problems</em></div> <div> <div class="panel panel-has-colored-body panel-has-border panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <iframe src="../../../pages/subjects/page-networks/index-62.htm?ticket=082b9c9c4ae3624d&network-id=20&sitename=physics&subject-id=6&fullscreen=false&node=start" style="width: 100%; height: 640px; max-height: 80vh" id="network-20" class="network-viewer"></iframe> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <iframe 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