Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 22 - Electromagnetic Waves - Problems - Page 642: 40

Answer

The range is from $2.7\times10^{-9}H$ to $4.0\times10^{-9}H$.

Work Step by Step

Equation 21-19 gives the resonant frequency of a LC circuit. $$f_o=\frac{1}{2 \pi}\sqrt{\frac{1}{LC}}$$ $$L=\frac{1}{4\pi^2Cf_o^2}$$ To find the range of L values, find the low and the high value of the inductance. $$L=\frac{1}{4\pi^2(810\times 10^{-12}F)(108\times10^6Hz)^2}=2.7\times10^{-9}H$$ $$L=\frac{1}{4\pi^2(810\times 10^{-12}F)(88\times10^6Hz)^2}=4.0\times10^{-9}H$$
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