davisnotes/elec_circuits_sp.html

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<title>Electricity - Series and Parallel Circuits - Physics 299</title>
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<h1> <img src="ULPhys1.gif" height="50" align="texttop"
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<h1>Series and Parallel Circuits<br>
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<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>
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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>
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<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>
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<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>
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</blockquote>
</blockquote>
<div align="left">
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<ul>
<li>
<h3><font color="#3333ff">Parallel</font></h3>
</li>
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<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>.&nbsp;
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>
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<img alt="fig2" src="elec_circuits_fig2.jpg" height="173"
width="312"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;
<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>
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<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.&nbsp; 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>
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<blockquote>
<div align="center"> </div>
</blockquote>
</blockquote>
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<font color="#ff0000"><i>Got mole problems? Call Avogadro at
602-1023.</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>
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