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 34 - Electromagnetic Fields and Waves - Exercises and Problems - Page 1031: 41

Answer

${\bf 20}\;\rm V$

Work Step by Step

Recalling, from the previous chapters, that the current through a discharged capacitor is given by $$I=I_{\rm max}e^{-t/\tau}$$ where $_{\rm max}$ is the maximum current which is given by $$I_{\rm max}=\dfrac{(\Delta V_C)_{\rm max}}{R}$$ where $\tau=RC$, so $R=\tau/C$; $$I_{\rm max}=\dfrac{C(\Delta V_C)_{\rm max}}{\tau }$$ Solving for $(\Delta V_C)_{\rm max}$; $$(\Delta V_C)_{\rm max}=\dfrac{\tau I_{\rm max}}{C}$$ From the given formula, we can see that $I_{\rm max}=10$ A, $\tau=2\;\mu$s. Plug the known into the previous formula, $$(\Delta V_C)_{\rm max}=\dfrac{ (2\times 10^{-6} )(10)}{(1\times 10^{-6})}$$ $$(\Delta V_C)_{\rm max}=\color{red}{\bf 20}\;\rm V$$
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