209 lines
7.7 KiB
HTML
209 lines
7.7 KiB
HTML
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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html;
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charset=windows-1252">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
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alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Magnetism - LR Circuits - Physics 299</title>
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<meta content="C. L. Davis" name="author">
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
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255);" link="#0000ee" vlink="#551a8b" alink="#ff0000">
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<center>
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<h1> <img src="ULPhys1.gif" height="50" width="189"
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align="texttop"></h1>
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</center>
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<center>
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<h1>LR Circuits<br>
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</h1>
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</center>
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<center><img src="celticbar.gif" height="22" width="576"><br>
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<br>
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<font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font>
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<div class="copy-paste-block"><font color="#ff0000"><i><span
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class="bqQuoteLink">"A</span></i></font><font
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color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
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statement that everyone believes. It is innocent,
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unless found guilty. A hypothesis is a novel
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suggestion that no one wants to believe. It is
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guilty, until found effective</span></i><span></span>"</font><br>
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</div>
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<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
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</center>
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<img src="netbar.gif" height="40" width="100%" align="middle">
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<blockquote> </blockquote>
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<ul>
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<li>As we have seen, due to Faraday's Law, an induced emf will
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appear in any loop/coil/circuit in which the current (and
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therefore the magnetic field) changes with time. Certain
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circuit elements have a larger (self) inductance than others -
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the solenoid is the most obvious example of a circuit element
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with a large inductance.</li>
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</ul>
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<ul>
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<li>An ideal inductance (L) has no resistance and is represented
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by the following symbol <img alt="magLRfig1"
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src="mag_LR_fig1.jpg" height="30" width="143" align="middle">
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.</li>
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</ul>
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<div align="left">
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<ul>
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<li><img alt="magLRfig2" src="mag_LR_fig2.jpg" height="207"
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width="300" align="right">Placing an inductance (L) and a
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resistance (R) in a simple circuit gives us the "LR" circuit,
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at right. When the switch is closed to include the power
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supply in the circuit we can apply Kirchoff's loop theorem to
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obtain the following equation,</li>
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</ul>
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<div align="center"><img alt="magLReqn1" src="mag_LR_eqn1.jpg"
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height="84" width="158"><br>
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<blockquote>
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<div align="left"><img alt="exclamation"
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src="exclamation-icon.gif" height="30" width="31"> Note
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that in applying the loop theorem we make use of the fact
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that the induced emf across the inductance opposes the
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changing emf that causes it. <br>
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</div>
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</blockquote>
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<div align="left">
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<ul>
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<li><img alt="magLRfig3" src="mag_LR_fig3.jpg" height="240"
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width="419" align="right">The solution of this
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differential equation is given by,</li>
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</ul>
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<div align="center"><img alt="magLReqn2" src="mag_LR_eqn2.jpg"
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height="57" width="236"><br>
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<blockquote>
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<div align="left">shown at right, where I<sub>max</sub> is
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ε/R . Also shown is the time dependence of
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the voltage across the inductance.<br>
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</div>
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</blockquote>
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<div align="left">
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<ul>
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<li>The time constant of the inductance, given by
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<img alt="magLReqn3" src="mag_LR_eqn3.jpg" height="38"
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width="112" align="middle"> is a measure of the time
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needed for the current in the circuit to reach 63% of
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its maximum value.</li>
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</ul>
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<p><br>
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</p>
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<ul>
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</ul>
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<ul>
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<li><img alt="magLRfig4" src="mag_LR_fig4.jpg"
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height="247" width="270" align="right">Taking the
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power supply out of the circuit leads to an even
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simpler differential equation<br>
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</li>
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</ul>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div align="center"><img alt="magLReqn4" src="mag_LR_eqn4.jpg"
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height="84" width="161"><br>
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<blockquote>
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<div align="left">the solution of which is<br>
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<div align="center"><img alt="magLReqn5" src="mag_LR_eqn5.jpg"
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height="57" width="180"><br>
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<div align="left">shown at right. In this figure I<sub>0</sub>
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= ε/R. </div>
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</div>
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</div>
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</blockquote>
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</div>
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<ol>
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</ol>
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<div align="left"> </div>
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<blockquote>
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<blockquote> </blockquote>
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</div>
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<div align="center"><img src="netbar.gif" height="40" width="100%"></div>
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<div align="center">
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<div align="center"> </div>
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<center>
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<p style="color: rgb(255, 0, 0); font-style: italic;"
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class="MsoNormal">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</p>
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<font color="#ff0000"><i>This girl said she recognized me from
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the vegetarian club, but I'd never met herbivore. </i></font><br>
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<br>
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<img src="celticbar.gif" height="22" width="576"> <br>
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<p><i>Dr. C. L. Davis</i> <br>
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<i>Physics Department</i> <br>
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<i>University of Louisville</i> <br>
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<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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<br>
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<p><img src="header-index.gif" height="51" width="92"> </p>
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</center>
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<blockquote> </blockquote>
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</div>
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</body>
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</html>
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