College Physics (7th Edition)

Published by Pearson
ISBN 10: 0-32160-183-1
ISBN 13: 978-0-32160-183-4

Chapter 16 - Electric Potential, Energy, and Capacitance - Learning Path Questions and Exercises - Conceptual Questions - Page 591: 16


a) charge gets doubled. b) increases by a factor of 4.

Work Step by Step

(a) $q_{1}=CV_{1}$ $q_{2}=CV_{2}$ Given that $V_{2}=2V_{1}$. Therefore, $q_{2}=C(2V_{1})=2CV_{1}=2q_{1}$ If the potential difference is doubled, charge also gets doubled. (b) $E_{1}=\frac{1}{2}CV_{1}^{2}$ $E_{2}=\frac{1}{2}CV_{2}^{2}$ Given that $V_{2}=2V_{1}$. Therefore, $E_{2}=\frac{1}{2}C(2V_{1})^{2}=4(\frac{1}{2}CV_{1}^{2})=4E_{1}$. Energy increases by a factor of 4.
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