What is the inductance of the inductor in a series RCL circuit with a resonant frequency of 640 Hz if the only other element in the circuit is a 1.2-µF capacitor?
A)52 mH
B)74 mH
C)0.12 H
D)2.1 H
E)13 H

Question

Quizplus · Accepted Answer

The resonant frequency $ f_0 $ of a series RCL circuit is given by the formula $ f_0 = \frac{1}{2\pi\sqrt{LC}} $. Rearranging for $ L $, we have $ L = \frac{1}{(2\pi f_0)^2 C} $. Substituting $ f_0 = 640 $ Hz and $ C = 1.2 \times 10^{-6} $ F, we find $ L \approx 52 $ mH.

What Is the Inductance of the Inductor in a Series