To double the resonant frequency of an LC circuit with a fixed value of L, the capacitance must be

Question

Question

This question was previously asked in

URSC ISRO Technical Assistant Electronics 20 August 2017 Official Paper

Answer 1

Concept:

An LC circuit is represented as:

F3 S.B Madhu 13.03.20 D5

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