A series RLC circuit in a radio is in resonance with AM 500 kHz.If the radio station is changed to AM 1500 kHz,by what factor must the capacitance be multiplied to again achieve resonance?
A) 9
B) 3
C) 1
D) 1/3
E) 1/9

Question

A series RLC circuit in a radio is in resonance with AM 500 kHz.If the radio station is changed to AM 1500 kHz,by what factor must the capacitance be multiplied to again achieve resonance?
A) ​9
B) 3
C) 1
D) 1/3
E) ​1/9

Quizplus · Accepted Answer

The resonant frequency of an RLC circuit is inversely proportional to the square root of the capacitance. To triple the frequency from 500 kHz to 1500 kHz, the capacitance must be reduced by a factor of 9 (since frequency is proportional to the inverse square root of capacitance, (f ∝ 1/√C)).

A Series RLC Circuit in a Radio Is in Resonance