In an LC oscillator, if values of inductance and capacitance become...

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes

\mathrm{x}

times its initial resonant frequency

\omega_0

. The value of

x

is:

Options

A $1 / 4$
B16
C $1 / 16$
D4

Correct answer

A. $1 / 4$

Step-by-step solution

The resonance frequency of LC oscillations circuit is

\omega=\frac{1}{\sqrt{\mathrm{L}^{\prime} \mathrm{C}^{\prime}}} \Rightarrow \mathrm{L}^{\prime} \rightarrow 2 \mathrm{ L}

\mathrm{C}^{\prime} \rightarrow 8 \mathrm{C}

\omega=\frac{1}{\sqrt{2 \mathrm{ L} \times 8 \mathrm{C}}}=\frac{1}{4 \sqrt{\mathrm{LC}}} 9 \omega_0=\frac{1}{\sqrt{\mathrm{LC}}}

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

So,

x=\frac{1}{4}

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