Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 19 - DC Circuits - Problems - Page 555: 63

Answer

$I=9.60\times10^{-4}A$ $V=4.8V$ $E_I=-20%$ $E_V=20%$

Work Step by Step

Net resistance of circuit is $R_{eq}=1.0\Omega+0.50\Omega+7.5k\Omega+(\frac{1}{15k\Omega}+\frac{1}{7.5k\Omega})^{-1}=12.5k\Omega$ The ammeter will read: $I=\frac{V}{R_{eq}}=\frac{12.0V}{12.5k\Omega}=9.60\times10^{-4}A$ The voltmeter will read: $R=(\frac{1}{15k\Omega}+\frac{1}{7.5k\Omega})^{-1}=5k\Omega$ $V=IR=(9.60\times10^{-4}A)(5k\Omega)=4.8V$ Without the voltmeter or ammeter, the net resistance of the circuit will be: $R_{eq}=1.0\Omega+0.50\Omega+2\times7.5k\Omega=15k\Omega$ and current will be: $I=\frac{V}{R_{eq}}=\frac{12.0V}{15k\Omega}=8.00\times10^{-4}A$ and voltage will be: $V=IR=(8.00\times10^{-4}A)(7.5k\Omega)=6.0V$ Percent error in current measure is: $E_I=\frac{8.00\times10^{-4}A-9.60\times10^{-4}A}{8.00\times10^{-4}A}\times100\%=-20%$ Percent error in voltage measure is: $E_V=\frac{6.0V-4.8V}{6.0V}\times100\%=20%$
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