To double the resonant frequency of an LC circuit with a fixed va
| To double the resonant frequency of an LC circuit with a fixed value of L, the capacitance must be
A. reduced by one quarter
B. reduced by one-half
C. doubled
D. quadrupled
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
An LC circuit is represented as:
There is a characteristic frequency at which the circuit will oscillate, called the resonant frequency given by:
\(f_{0}=\frac{1}{2\pi\sqrt{LC}}\)
Application:
For a fixed value of L, the resonant frequency is proportional to:
\(f_{0}\propto\frac{1}{\sqrt{C}}\)
To double the resonant frequency, C must be reduced to 1/4 (quarter), i.e. for C' = C/4, f0 becomes:
f'0 = 2 f0
