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 - Questions - Page 618: 26

Answer

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Work Step by Step

a. The frequency of the source emf does not affect the impedance of a pure resistance. R is independent of the source emf frequency. b. The impedance of a pure capacitance varies inversely with the frequency of the source emf, $X_C=1/2\pi f C$. If the source frequency is very small, the impedance of the capacitor is very large, and vice versa. c. The impedance of a pure inductance is proportional to the frequency of the source emf, $X_L=2\pi f L$. If the source frequency is very small, the impedance of the inductor is very small, and vice versa. d. The impedance of an LRC circuit near resonance (small R) is very sensitive to the frequency of the source emf. This is discussed in section 21-15, and Figure 21-46 shows that the impedance rises rapidly as the source frequency is changed by just a small amount around resonance. e. The impedance of an LRC circuit far from resonance (small R) depends upon the frequency of the source emf. This is discussed in section 21-15, and Figure 21-46 summarizes the dependence. If the source frequency f is much higher than the resonance frequency, the impedance is proportional to the frequency of the source emf. Equation 21-15 shows that at high f, the circuit impedance is dominated by the inductance, and $Z \approx X_L=2\pi f L$. On the other hand, if the source frequency f is much lower than the resonance frequency, then the impedance is inversely proportional to the frequency of the source emf. Equation 21-15 shows that at low f, the circuit impedance is dominated by the capacitance, and $Z \approx X_C =1/2\pi f C $.
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