Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 31 - Electromagnetic Oscillations and Alternating Current - Problems - Page 938: 49d

Answer

The resonant frequency increases if $C_3$ is removed.

Work Step by Step

We can find the equivalent capacitance of three capacitors in parallel: $C = C_1+C_2+C_3 = 4.00~\mu F+2.50~\mu F+3.50~\mu F = 10.0~\mu F$ We can find the equivalent inductance of two inductors in series: $L = L_1+L_2 = 1.70~mH+2.30~mH = 4.00~mH$ We can find an expression for the original resonant frequency: $\omega_d = \frac{1}{\sqrt{L~C}}$ $2\pi~f_d = \frac{1}{\sqrt{L~C}}$ $f_d = \frac{1}{2\pi~\sqrt{L~C}}$ If $C_3$ is removed, then the equivalent capacitance $C$ decreases, which in turn increases the resonant frequency. The resonant frequency increases if $C_3$ is removed.
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