Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 29 - Potential and Field - Exercises and Problems - Page 864: 52

Answer

$25\;\rm \mu F$

Work Step by Step

First, we need to re-sketch this circuit and reduce it as we see in the figures below. The two capacitors, in the first circuit below, $C_1$ and $C_2$ are in series so their equivalent is given by $$(C_{eq})_{12 }=\left[ \dfrac{1}{C_1}+\dfrac{1}{C_2} \right]^{-1}$$ Plug the known; $$(C_{eq})_{12}=\left[ \dfrac{1}{20}+\dfrac{1}{30} \right]^{-1}$$ $$(C_{eq})_{12 }=\color{black}{\bf 12}\;\rm \mu F$$ The two capacitors, in the second circuit below, $(C_{eq})_{23}$ and $C_3$ are in parallel so their equivalent is given by $$(C_{eq})_{123}=(C_{eq})_{23}+C_3=12+13$$ $$(C_{eq})_{123 }=\color{red}{\bf 25}\;\rm \mu F$$
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