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  4. 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 ω0. The value of x is:

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Q. 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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Solution:

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 $x=\frac{1}{4}$