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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/hybrid.jpg" style="float: left; width: 250px; height: 140px;">Electromagnetic induction is the process by which kinetic energy is converted into electrical energy in the presence of a magnetic field.</p> <p>How can we determine the magnitude and direction of induced EMF? What is involved in the construction and operation of an AC generator? How is electrical power transmitted across countries? What can we do to convert AC to DC? What is a capacitor?</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"> <p>Electromagnetic induction is the process by which an EMF is induced due to the relative motion of a magnetic field and conductor.</p> <p><a href="../1143/faradays-law.html">Faraday's law</a> and <a href="../1142/lenzs-law.html">Lenz's law</a> can be combined to determine the magnitude and direction of the induced EMF:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon =-{\mathrm{d}N\Phi\over \mathrm{d}t}\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon \)</span> is the induced EMF (V)</li> <li><span class="math-tex">\(N\Phi\)</span> is the magnetic flux linkage (Tm<sup>2</sup> or Wb)</li> <li><span class="math-tex">\({\mathrm{d}N\Phi\over \mathrm{d}t}\)</span> is the rate of change of magnetic flux linkage (Tm<sup>2</sup>s<sup>-1</sup> or Wb s<sup>-1</sup>)</li> </ul> <p style="text-align: center;"><img alt="" src="../../em-induction/righthandoutline.png" style="height: 182px; width: 250px;"></p> <div class="panel panel-turquoise 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>AC generators</p> </div> </div> <div class="panel-body"> <div> <h4>Construction</h4> <p>An <a href="../1141/ac-generators.html">AC generator</a> consists of a rotating coil inside a magnetic field. The angle of the coil within the field affects the size and direction of the current induced; the current output is sinusoidal.</p> <p style="text-align: center;"><img alt="" src="../../em-induction/ac-generator.png" style="height: 173px; width: 350px;"></p> <h4>Induced current and EMF</h4> <p>To perform calculations with the induced current and EMF, root mean square quantities are used:</p> <p style="text-align: center;"><span class="math-tex">\(I_\text{rms}={I_0\over \sqrt2}\)</span></p> <ul> <li><span class="math-tex">\(I_\text{rms}\)</span> is the root mean square current (A)</li> <li><span class="math-tex">\(I_0\)</span> is the maximum magnitude of the current in either direction (A)</li> </ul> <p style="text-align: center;"><span class="math-tex">\(V_\text{rms}={V_0\over \sqrt2}\)</span></p> <ul> <li><span class="math-tex">\(V_\text{rms}\)</span> is the root mean square potential difference (V)</li> <li><span class="math-tex">\(V_0\)</span> is the maximum magnitude of the potential difference (V)</li> </ul> <p style="text-align: center;"><span class="math-tex">\(R={V_0\over I_0}={V_\text{rms}\over I_\text{rms}}\)</span></p> <ul> <li><span class="math-tex">\(R\)</span> is the resistance (<span class="math-tex">\(\Omega\)</span>)</li> </ul> <p style="text-align: center;"><span class="math-tex">\(P_\text{max}=I_0V_0\)</span></p> <ul> <li><span class="math-tex">\(P_\text{max}\)</span> is the maximum power (W)</li> </ul> <p style="text-align: center;"><span class="math-tex">\(\bar{P}={1\over 2}I_0V_0\)</span></p> <ul> <li><span class="math-tex">\(\bar{P}\)</span> is the average power (W)</li> </ul> <h4>AC generator equation</h4> <p>The size of the EMF induced varies according to the AC generator equation:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon=BAN\omega \sin{\omega t}\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon\)</span> is the EMF at a given time (V)</li> <li><span class="math-tex">\(B\)</span> is magnetic flux density (T)</li> <li><span class="math-tex">\(A\)</span> is the perpendicular area of the coil in the field (m<sup>2</sup>)</li> <li><span class="math-tex">\(N\)</span> is the number of turns on the coil</li> <li><span class="math-tex">\(\omega\)</span> is angular velocity (rad s<sup>-1</sup>)</li> <li><span class="math-tex">\(t\)</span> is time, with <span class="math-tex">\(t=0\)</span> for the coil sides rotating parallel to the field</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise 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>Transformers</p> </div> </div> <div class="panel-body"> <div> <p><a href="../1140/transformers.html">Transformers</a> are used in electrical power transmission to increase voltage and decrease current (step-up) or to decrease voltage (step-down). The nature of the transformer depends on the ratio of turns between the primary and secondary coils:</p> <p style="text-align: center;"><img alt="" src="../../em-induction/transformer3d_col3.svg" style="height: 263px; width: 350px;"></p> <p>For an ideal transformer:</p> <p style="text-align: center;"><span class="math-tex">\({\varepsilon_p\over \varepsilon_s}={N_p\over N_s}={I_s\over I_p}\)</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> </div> <div class="panel-footer"> <div> <p> </p> </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-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>Rectification</p> </div> </div> <div class="panel-body"> <div> <p>Alternating current can be converted into direct current by <a href="../1137/diodes-and-rectification.html">rectification</a>:</p> <ul> <li>In half wave rectification, a diode is inserted. Current will only pass in forward bias.</li> <li>In full wave rectification, two diode pathways are inserted. Current will pass in either direction, but will always enter the load resistor at the same side.</li> <li>The addition of a capacitor to a diode bridge rectification circuit creates a smoothing effect.</li> </ul> <p style="text-align: center;"><img alt="" src="../../em-induction/half.png" style="width: 336px; height: 200px;"><img alt="" src="../../em-induction/full.png" style="width: 242px; height: 200px;"></p> <p>Diodes are made from semiconducting materials containing a p-n junction.</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>Capacitors</p> </div> </div> <div class="panel-body"> <div> <h4>Capacitance</h4> <p>The capacitance of a <a href="../1136/capacitors.html">capacitor</a> is defined as the ratio of the charge stored to the potential difference across the capacitor:</p> <p style="text-align: center;"><span class="math-tex">\(C={q\over V}\)</span></p> <ul> <li><span class="math-tex">\(C\)</span> is capacitance (F)</li> <li><span class="math-tex">\(q\)</span> is charge (C)</li> <li><span class="math-tex">\(V\)</span> is potential difference (V)</li> </ul> <p style="text-align: center;"><span class="math-tex">\(E={1\over 2}CV^2\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is the energy stored on the capacitor or the work done that was required to store the charges (J)</li> </ul> <h4>Charging and discharging</h4> <p>Capacitors can be charged and discharged using a two-way switch circuit:</p> <p style="text-align: center;"><img alt="" src="../../em-induction/discharge-capacitor-circuit-diagram-1.png" style="height: 211px; width: 200px;"></p> <p>When discharging, the charge, current and potential difference decay exponentially over time:</p> <p style="text-align: center;"><span class="math-tex">\(q=q_0e^{-t\over \tau}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(I=I_0e^{-t\over \tau}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(V=V_0e^{-t\over \tau}\)</span></p> <ul> <li><span class="math-tex">\(q\)</span> is the remaining charge stored on the capacitor (C)</li> <li><span class="math-tex">\(q_0\)</span> is the initial charge stored on the capacitor (C)</li> <li><span class="math-tex">\(I\)</span> is the current (A)</li> <li><span class="math-tex">\(I_0\)</span> is the initial current (A)</li> <li><span class="math-tex">\(V\)</span> is the potential difference across the capacitor (C)</li> <li><span class="math-tex">\(V_0\)</span> is the initial potential difference across the capacitor (C)</li> <li><span class="math-tex">\(t\)</span> is the time over which the capacitor has been discharging (s)</li> <li><span class="math-tex">\(\tau\)</span> is the time constant (s)</li> </ul> <p style="text-align: center;"><img alt="" src="../../em-induction/discharge.png" style="height: 141px; 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</textarea></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary btn-xs-block save-notes"><i class="fa fa-fw fa-pencil"></i>Save</button><button type="button" class="btn btn-sm btn-default btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div><div id="report-problem-sm-modal" class="modal fade overlay-modal report-problem" tabindex="-1" role="dialog"><div class="modal-dialog modal-sm" role="document"><div class="modal-content"><div class="modal-header p-xs-3"><h4 class="modal-title text-center my-xs-2">Report a problem for flashcard <span class="fc-viewer-id"></span></h4></div><div class="modal-body p-xs-3"><div class="msg"></div><div class="form-group mb-xs-0"><textarea class="form-control issue-description p-xs-3" rows="8"></textarea></div></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary text-center btn-xs-block mb-xs-3 disabled send-report"><i class="fa fa-fw fa-paper-plane"></i>Send</button><button type="button" class="btn btn-sm btn-default text-center btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div> <div id="fcgame-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"> <div class="modal-dialog modal-lg modal-dialog-fcgame" role="document"> <div class="modal-content mc-flashcard modal-content-fcgame"> <div class="modal-header" style="background-color: #fafafa;"> <div class="row text-center" style="width: 100%;"> <div class="col-md-12"> <div style="display: flex; justify-content: space-between; align-items: center;"> <div class="text-left"> Your time: <span class="chronometer c-mobile" id="chronometer">00:00:</span> <span class="chronometer msec c-mobile" id="chronometer-msec">000</span> <br> Your best time: <span class="chronometer c-mobile" id="best-record"></span> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span 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