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fa-fw fa-chevron-right divider"></i></li><li><span class="gray">AC generators</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/generator.jpg" style="float: left; width: 250px; height: 202px;"></p> <p>Most of the world's electrical power is generated using electrical generators.</p> <p>Generators convert rotational kinetic energy (usually powered by a turbine) into electrical energy using electromagnetic induction.</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 class="panel panel-turquoise panel-has-colored-body panel-has-border"> <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 basic AC generator operates by the rotation of a coil within a magnetic field. This diagram shows the coil being rotated by a handle, which could represent a turbine.</p> <p style="text-align: center;"><img alt="" src="../../em-induction/ac-generator.png" style="height: 173px; width: 350px;"></p> <p>The left side of this coil is moving upwards. The magnetic field direction is from north to south. Using Fleming's right hand rule, we can determine that a current would be induced in the direction away from the handle. The converse is true for the right side of the coil.</p> <p>When the coil has rotated 90<sup>o</sup>, the motion of the sides will be parallel to the field lines. No current is induced.</p> <p>After a 180<sup>o</sup> rotation, the current will again be maximised, but the direction around the coil will be opposite to its initial direction. The slip rings enable the coil to spin continuously and for this alternating current to be transmitted.</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/369633986"></iframe></div> </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>Types of current</p> </div> </div> <div class="panel-body"> <div> <p>The current produced by the generator described above is alternating. Alternating current is defined by the repeated cyclical change of direction (not just by a change in magnitude).</p> <p style="text-align: center;"><img alt="" src="../../em-induction/ac-dc.png" style="height: 190px; width: 350px;"></p> <p>Direct current, which travels in a constant direction, can be produced by a dynamo.</p> </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>EMF in a rotating coil</p> </div> </div> <div class="panel-body"> <div> <p>Although not required for the exam, it is helpful to be familiar with the equation for the EMF induced in a rotating coil. Conveniently, we have already defined the flux for a given angle:</p> <p style="text-align: center;"><span class="math-tex">\(\Phi=BA\cos\theta\)</span></p> <p>Flux linkage, <span class="math-tex">\(N\Phi=BAN\cos\theta\)</span> and, for a given time, <span class="math-tex">\(\theta=\omega t\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow N\Phi=BAN\cos{\omega t}\)</span></p> <p>The EMF is the negative of the rate of change of flux linkage, <span class="math-tex">\(\varepsilon=-{\mathrm{d}N\Phi\over \mathrm{d}t}\)</span>. Mathematicians will be familiar with differentiating trigonometric functions.</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> <p>The maximum of this equation is when <span class="math-tex">\(\sin{\omega t}=1\)</span>:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon_0=BAN\omega\)</span></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/369634129"></iframe></div> </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>Calculations</p> </div> </div> <div class="panel-body"> <div> <p>Because alternating current has equal magnitudes and equal times in opposite directions, the true mean average potential difference and current are zero. However, clearly the electrical power generated can be transmitted and used.</p> <p>We therefore use another type of average, root mean square:</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>The definition of <a href="../184/resistance.html" title="Resistance">Resistance</a> is unchanged; it is the ratio of the potential difference across a conductor to the current flowing through it at an instant:</p> <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>The electrical power produced is the product of the current and voltage. For maximum power, when the rotation of the coil is perpendicular to the magnetic field:</p> <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>The average power is the product of the root mean square current and potential difference:</p> <p style="text-align: center;"><span class="math-tex">\(\bar{P}={I_0\over \sqrt2}{V_0\over \sqrt2}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow\bar{P}={1\over 2}I_0V_0\)</span></p> <ul> <li><span tabindex="-1"></span><span class="math-tex">\(\bar{P}\)</span> is the average power (W)</li> </ul> <p>All of these equations are found in the data booklet and can be used to solve problems for an AC circuit.</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>Effect of changing frequency</p> </div> </div> <div class="panel-body"> <div> <p>From the equation it is easily to identify that increasing magnetic flux density, the area of the coil and the number of turns will increase the induced EMF. But what about frequency?</p> <p>Angular velocity, <span class="math-tex">\(\omega\)</span>, depends on frequency, so increasing frequency has two effects:</p> <ol> <li>The size of the EMF increases</li> <li>The time between peaks decreases</li> </ol> <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/369634181"></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-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Root mean square</p> </div> </div> <div class="panel-body"> <div> <p>A root mean square quantity has the same dimension as the quantity itself. This is because the quantity is sqared at all instances (and thus becomes entirely positive) and is then rooted.</p> <p>You are not expected to know the proof of the relationship, but may find this video interesting.</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/369633956"></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 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 flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="" data-topics="1006" data-subject-id="6" data-n-flashcards="8" style="text-align:center">Show flashcards</a></div><hr> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1141"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>AC generators</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/1141/ac-generators"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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