In a RLC circuit, the values of the inductance and capacitance are both doubled. 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 a RLC circuit is given by:

fr = 1 / 2π√(LC)

If both L and C are doubled, the new resonant frequency is:

fr' = 1 / 2π√(2L * 2C)

fr' = 1 / 2π√(4LC)

fr' = 1 / 2π(2√LC)

fr' = 1 / (√LC) * (1 / 2π)

fr' = fr / √2

So the new resonant frequency is reduced to one-half the original value, which is option B.

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