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: 65

Answer

270 Hz.

Work Step by Step

Calculate the rms current through the circuit by using the rms voltage across the resistor. $$I_{rms}=\frac{V_{R,rms}}{R}$$ Use the rms current with the rms voltage across the capacitor, equation 21–13b, and find the frequency. $$V_{C,rms}=\frac{I_{rms}}{2\pi f C}$$ $$f=\frac{I_{rms}}{2\pi C V_{C,rms}}$$ $$f=\frac{V_{R,rms}}{R 2\pi C V_{C,rms}}$$ $$f=\frac{3.0V}{(650\Omega) 2\pi (1.0\times10^{-6}F)(2.7V)}\approx 270Hz$$ The sinusoidal voltages across the resistor and across the capacitor are not in phase. Therefore, we wouldn’t expect the rms voltage across the power source to be the sum of the rms voltages across the resistor and across the capacitor.
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