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 35 - AC Circuits - Exercises and Problems - Page 1052: 26

Answer

${\bf 10.1}\;\rm mL$

Work Step by Step

We know, for $RLC$-circuits, that the resonance frequency occurs when $$X_L=X_C$$ $$2\pi f L=\dfrac{1}{2\pi f C}$$ Hence, $$ f^2 =\dfrac{1}{4\pi^2 L C}$$ Solving for $L$, $$ L =\dfrac{1}{4\pi^2 f^2 C}$$ Plug the known; $$ L =\dfrac{1}{4\pi^2 (1000)^2 (2.5\times 10^{-6})}$$ $$L=\color{red}{\bf 10.1}\;\rm mL$$
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