davisnotes/mag_LR.html

209 lines
7.7 KiB
HTML
Raw Normal View History

2016-05-20 00:56:25 -04:00
<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html;
charset=windows-1252">
<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
alpha) [Netscape]">
<meta name="Author" content="C. L. Davis">
<title>Magnetism - LR Circuits - Physics 299</title>
<meta content="C. L. Davis" name="author">
</head>
<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
255);" link="#0000ee" vlink="#551a8b" alink="#ff0000">
<center>
<h1> <img src="ULPhys1.gif" height="50" width="189"
align="texttop"></h1>
</center>
<center>
<h1>LR Circuits<br>
</h1>
</center>
<center><img src="celticbar.gif" height="22" width="576"><br>
<br>
<font color="#ff0000"><i>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</i></font><font color="#ff0000"><i>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</i></font>
<div class="copy-paste-block"><font color="#ff0000"><i><span
class="bqQuoteLink">"A</span></i></font><font
color="#ff0000"><i><span class="bqQuoteLink"> fact is a simple
statement that everyone believes.&nbsp; It is innocent,
unless found guilty.&nbsp; A hypothesis is a novel
suggestion that no one wants to believe.&nbsp; It is
guilty, until found effective</span></i><span></span>"</font><br>
</div>
<font color="#ff0000"><i> </i><font color="#000000">Edward Teller</font></font><br>
</center>
<img src="netbar.gif" height="40" width="100%" align="middle">
<blockquote> </blockquote>
<ul>
<li>As we have seen, due to Faraday's Law, an induced emf will
appear in any loop/coil/circuit in which the current (and
therefore the magnetic field) changes with time.&nbsp; Certain
circuit elements have a larger (self) inductance than others -
the solenoid is the most obvious example of a circuit element
with a large inductance.</li>
</ul>
<ul>
<li>An ideal inductance (L) has no resistance and is represented
by the following symbol&nbsp; <img alt="magLRfig1"
src="mag_LR_fig1.jpg" height="30" width="143" align="middle">
.</li>
</ul>
<div align="left">
<ul>
<li><img alt="magLRfig2" src="mag_LR_fig2.jpg" height="207"
width="300" align="right">Placing an inductance (L) and a
resistance (R) in a simple circuit gives us the "LR" circuit,
at right.&nbsp; When the switch is closed to include the power
supply in the circuit we can apply Kirchoff's loop theorem to
obtain the following equation,</li>
</ul>
<div align="center"><img alt="magLReqn1" src="mag_LR_eqn1.jpg"
height="84" width="158"><br>
<blockquote>
<div align="left"><img alt="exclamation"
src="exclamation-icon.gif" height="30" width="31"> Note
that in applying the loop theorem we make use of the fact
that the induced emf across the inductance opposes the
changing emf that causes it. <br>
</div>
</blockquote>
<div align="left">
<ul>
<li><img alt="magLRfig3" src="mag_LR_fig3.jpg" height="240"
width="419" align="right">The solution of this
differential equation is given by,</li>
</ul>
<div align="center"><img alt="magLReqn2" src="mag_LR_eqn2.jpg"
height="57" width="236"><br>
<blockquote>
<div align="left">shown at right, where I<sub>max</sub> is
&#949;/R&nbsp; .&nbsp; Also shown is the time dependence of
the voltage across the inductance.<br>
</div>
</blockquote>
<div align="left">
<ul>
<li>The time constant of the inductance, given by&nbsp;
<img alt="magLReqn3" src="mag_LR_eqn3.jpg" height="38"
width="112" align="middle"> is a measure of the time
needed for the current in the circuit to reach 63% of
its maximum value.</li>
</ul>
<p><br>
</p>
<ul>
</ul>
<ul>
<li><img alt="magLRfig4" src="mag_LR_fig4.jpg"
height="247" width="270" align="right">Taking the
power supply out of the circuit leads to an even
simpler differential equation<br>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div align="center"><img alt="magLReqn4" src="mag_LR_eqn4.jpg"
height="84" width="161"><br>
<blockquote>
<div align="left">the solution of which is<br>
<div align="center"><img alt="magLReqn5" src="mag_LR_eqn5.jpg"
height="57" width="180"><br>
<div align="left">shown at right.&nbsp; In this figure I<sub>0</sub>
= &#949;/R. </div>
</div>
</div>
</blockquote>
</div>
<ol>
</ol>
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left"> </div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<blockquote>
<div align="left"> </div>
</blockquote>
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="left">
<div align="center">
<div align="center">
<div>
<div align="left">
<div align="center">
<div align="left"> </div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<blockquote>
<div align="left"> </div>
</blockquote>
</div>
</div>
<blockquote> </blockquote>
</div>
<div align="center"><img src="netbar.gif" height="40" width="100%"></div>
<div align="center">
<div align="center"> </div>
<center>
<p style="color: rgb(255, 0, 0); font-style: italic;"
class="MsoNormal">
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
</p>
<font color="#ff0000"><i>This girl said she recognized me from
the vegetarian club, but I'd never met herbivore. </i></font><br>
<br>
&nbsp;<img src="celticbar.gif" height="22" width="576"> <br>
&nbsp;
<p><i>Dr. C. L. Davis</i> <br>
<i>Physics Department</i> <br>
<i>University of Louisville</i> <br>
<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
<br>
&nbsp; </p>
<p><img src="header-index.gif" height="51" width="92"> </p>
</center>
<p><br>
</p>
<blockquote> </blockquote>
</div>
</body>
</html>