Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 24 - Alternating-Current Circuits - Conceptual Questions - Page 867: 11

Answer

Yes

Work Step by Step

We know that the impedance of $RLC$ circuit is given as $Z=\sqrt{R^2+(X_L-X_c)^2}$. The impedance depends on $X_L$ and $X_C$. At resonance $X_L=X_C$. Below the resonance condition $X_L\lt X_C$, so we have $X_L-X_C\lt 0$. Beyond the resonance condition $X_L\gt X_C$, so we have $X_L-X_C\gt 0$. Thus, there are two values of $\omega$ for which $(X_L-X_C)^2$ have the same value; one is below the resonance frequency and the other is above the resonance frequency.
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