Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 20 - Electric Potential and Electric Potential Energy - Problems and Conceptual Exercises - Page 721: 79

Answer

The capacitance is divided by four.

Work Step by Step

The capacitance of a parallel-plate capacitor is equal to $$C=\frac{\epsilon_o A}{d}$$ If the new area $A'=\frac{1}{2}A$ and the new distance of separation $d'=2d$, the new capacitance $C'$ equals $$C'=\frac{\epsilon_o(\frac{1}{2}A)}{2d}=\frac{\epsilon_o A}{4d}=\frac{1}{4}(\frac{\epsilon_o A}{d})=\frac{1}{4}C$$ Therefore, the capacitance is divided by four.
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