University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 26 - Direct-Current Circuits - Problems - Exercises - Page 873: 26.7

Answer

0.77 A

Work Step by Step

The two resistors $R_{1}$ and $R_{3}$ are in parallel and their combination is \begin{align*} R_{\text{13}} = \dfrac{R_{1}R_{3}}{R_{1} + R_{3} } = \dfrac{(45.0 \mathrm{~\Omega})(15.0 \mathrm{~\Omega})}{45.0 \mathrm{~\Omega} + 15.0 \mathrm{~\Omega} } = 11.25 \mathrm{~\Omega} \end{align*} This equivalent resistance is in series with $R_2$ and the internal resistance of the battery $r$, so we use Ohm's law to get the current that measured by the ammeter as \begin{align*} I = \dfrac{\varepsilon}{R_{13} + R_{2} + r} = \dfrac{25.0 \,\text{V}}{11.25 \mathrm{~\Omega} + 18.0 \mathrm{~\Omega}+ 3.26 \mathrm{~\Omega}} =\boxed{ 0.77 \,\text{A}} \end{align*}
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