In an \(LC\) oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes \(x\) times its initial resonant frequency \(\omega_0\). The value of \(x\) is:

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Answer & Solution

Correct Answer

(A) \(\frac{1}{4}\)

Detailed explanation

The resonance frequency of LC oscillations circuit is

\(\omega_0=\frac{1}{\sqrt{ LC }}\)

\(L \rightarrow 2 L\)

\(C \rightarrow 8 C\)

\(\omega=\frac{1}{\sqrt{2 L \times 8 C }}=\frac{1}{4 \sqrt{ LC }}\)

\(\omega=\frac{\omega_0}{4}\)

So \(x =\frac{1}{4}\)

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