141 lines
5.2 KiB
HTML
141 lines
5.2 KiB
HTML
|
<!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>Electricity - Series and Parallel 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" alink="#ff0000" vlink="#551a8b">
|
||
|
|
<center>
|
||
|
|
<h1> <img src="ULPhys1.gif" height="50" align="texttop"
|
||
|
|
width="189"></h1>
|
||
|
|
</center>
|
||
|
|
<center>
|
||
|
|
<h1>Series and Parallel Circuits<br>
|
||
|
|
</h1>
|
||
|
|
</center>
|
||
|
|
<center><img src="celticbar.gif" height="22" width="576"><br>
|
||
|
|
<br>
|
||
|
|
<font color="#ff0000"><i>"</i></font><font color="#ff0000"><i> </i></font><font
|
||
|
|
color="#ff0000"><i>
|
||
|
|
<meta http-equiv="content-type" content="text/html;
|
||
|
|
charset=windows-1252">
|
||
|
|
It would be better for the true physics if there were no
|
||
|
|
mathematicians on earth." <br>
|
||
|
|
</i><font color="#000000">Daniel Bernoulli</font></font><br>
|
||
|
|
</center>
|
||
|
|
<img src="netbar.gif" height="40" align="middle" width="100%"> <br>
|
||
|
|
<ul>
|
||
|
|
<li>You may already be familiar with the idea of circuits with
|
||
|
|
resistors in series or parallel or some combination of the two.</li>
|
||
|
|
</ul>
|
||
|
|
<ul>
|
||
|
|
<ul>
|
||
|
|
<li>
|
||
|
|
<h3><font color="#3333ff">Series</font></h3>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
</ul>
|
||
|
|
<blockquote>
|
||
|
|
<blockquote><img alt="fig1" src="elec_circuits_fig1.jpg"
|
||
|
|
height="168" align="right" width="273">The same current flows
|
||
|
|
in each resistor, the voltages across them are typically
|
||
|
|
different, where V = V<sub>1</sub> + V<sub>2</sub> + V<sub>3</sub>
|
||
|
|
which leads to the equivalent resistance formula<br>
|
||
|
|
<br>
|
||
|
|
<div align="center">R<sub>eq</sub> = R<sub>1</sub> + R<sub>2</sub>
|
||
|
|
+ R<sub>3</sub><br>
|
||
|
|
</div>
|
||
|
|
</blockquote>
|
||
|
|
</blockquote>
|
||
|
|
<div align="left">
|
||
|
|
<ul>
|
||
|
|
<ul>
|
||
|
|
<li>
|
||
|
|
<h3><font color="#3333ff">Parallel</font></h3>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
</ul>
|
||
|
|
<blockquote>
|
||
|
|
<blockquote>The potential difference across each resistor is the
|
||
|
|
same, but the currents through them are typically different,
|
||
|
|
where I = I<sub>1</sub> + I<sub>2</sub> + I<sub>3</sub>.
|
||
|
|
This lead to the equivalent resistance formula,<br>
|
||
|
|
<div align="center"><img alt="eqn1"
|
||
|
|
src="elec_circuits_eqn1.jpg" height="58" width="152"><br>
|
||
|
|
<br>
|
||
|
|
<div align="left">Note that both of the diagrams below
|
||
|
|
represent resistors in parallel.<br>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<img alt="fig2" src="elec_circuits_fig2.jpg" height="173"
|
||
|
|
width="312">
|
||
|
|
|
||
|
|
<img alt="fig3" src="elec_circuits_fig3.jpg" height="179"
|
||
|
|
width="301"><br>
|
||
|
|
<br>
|
||
|
|
</blockquote>
|
||
|
|
</blockquote>
|
||
|
|
<ul>
|
||
|
|
<ul>
|
||
|
|
<li>
|
||
|
|
<h3><font color="#3333ff">Combinations</font></h3>
|
||
|
|
</li>
|
||
|
|
</ul>
|
||
|
|
</ul>
|
||
|
|
<blockquote>
|
||
|
|
<blockquote>Some circuits can be analysed as combinations of
|
||
|
|
series and parallel circuits. In the circuit below R<sub>2</sub>
|
||
|
|
and R<sub>3</sub> are in parallel, their equivalent resistance
|
||
|
|
is then in series with R<sub>1</sub>.<br>
|
||
|
|
<div align="center"><img alt="fig4"
|
||
|
|
src="elec_circuits_fig4.jpg" height="181" width="390"><br>
|
||
|
|
</div>
|
||
|
|
</blockquote>
|
||
|
|
<img alt="exclamation" src="exclamation-icon.gif" height="30"
|
||
|
|
width="31"> Note that it is not possible to represent all
|
||
|
|
circuits as combinations of series and parallel elements, this
|
||
|
|
is most obvious in many cases where there is more than one
|
||
|
|
battery in the circuit, see example below. To analyse this
|
||
|
|
type of circuit we must use Kirchhoff's Laws.<br>
|
||
|
|
<br>
|
||
|
|
<div align="center"><img alt="fig5" src="elec_circuits_fig5.jpg"
|
||
|
|
height="185" width="435"><br>
|
||
|
|
</div>
|
||
|
|
<div align="center"><br>
|
||
|
|
</div>
|
||
|
|
<blockquote>
|
||
|
|
<div align="center"> </div>
|
||
|
|
</blockquote>
|
||
|
|
</blockquote>
|
||
|
|
</div>
|
||
|
|
<img src="netbar.gif" height="40" width="100%">
|
||
|
|
<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>Got mole problems? Call Avogadro at
|
||
|
|
602-1023.</i></font><br>
|
||
|
|
<br>
|
||
|
|
<img src="celticbar.gif" height="22" width="576"> <br>
|
||
|
|
|
||
|
|
<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>
|
||
|
|
</p>
|
||
|
|
<p><img src="header-index.gif" height="51" width="92"> </p>
|
||
|
|
</center>
|
||
|
|
<p><br>
|
||
|
|
</p>
|
||
|
|
</body>
|
||
|
|
</html>
|