In a RLC circuit, the values of the inductance and capacitance are both halved. In comparison with the resonance frequency of the original circuit, the new resonant frequency will be
A) the same as before.
B) reduced to one-half the original value.
C) reduced to one-quarter the original value.
D) increased by a factor of two.
E) increased by a factor of four.

Question

Quizplus · Accepted Answer

The resonant frequency of an RLC circuit is given by $ f_0 = \frac{1}{2\pi\sqrt{LC}} $. If both L and C are halved, the new frequency becomes $ f_0' = \frac{1}{2\pi\sqrt{(L/2)(C/2)}} = \frac{1}{2\pi\sqrt{LC/4}} = 2f_0 $. Thus, the resonant frequency is increased by a factor of two.

In a RLC Circuit, the Values of the Inductance and Capacitance