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: 51

Answer

$7.5\;\rm \mu F$

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, $C_2$ and $C_3$ are in parallel so their equivalent is given by $$(C_{eq})_{23}=C_2+C_3=20+10$$ $$(C_{eq})_{23}=\bf 30\;\rm \mu F\tag 2$$ The two capacitors, in the second circuit below, $C_1$ and $(C_{eq})_{23}$ are in series so their equivalent is given by $$(C_{eq})_{123}=\left[ \dfrac{1}{C_1}+\dfrac{1}{(C_{eq})_{23}} \right]^{-1}$$ Plug the known; $$(C_{eq})_{123}=\left[ \dfrac{1}{10}+\dfrac{1}{30} \right]^{-1}$$ $$(C_{eq})_{123}=\color{red}{\bf 7.5}\;\rm \mu F$$
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