Physics: Principles with Applications (7th Edition)

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

Chapter 21 - Electromagnetic Induction and Faraday's Law - Problems - Page 622: 70

Answer

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Work Step by Step

a. Equation 21-19 gives the resonant frequency. $$f_o=\frac{1}{2 \pi}\sqrt{\frac{1}{LC}}$$ Take ratios. $$\frac{f_{580}}{ f_{1600}}=\frac{580kHz}{1600kHz}=\frac{\frac{1}{2 \pi}\sqrt{\frac{1}{LC_{580}}}}{\frac{1}{2 \pi}\sqrt{\frac{1}{LC_{1600}}}}$$ $$C_{1600}=\frac{580^2}{1600^2}C_{580}=\frac{580^2}{1600^2}2800pF\approx 370pF$$ b. Calculate the inductance using the resonant frequency and the capacitance. $$L=\frac{1}{4\pi^2 f^2 C}$$ $$L=\frac{1}{4\pi^2 (5.8\times10^5 Hz)^2 (2800\times10^{-12}F)}= 2.7\times10^{-5}H $$
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