In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of the oscillator becomes times its initial resonance frequency . The value of is [2023]

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Solution

Q.
In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of the oscillator becomes $' x'$ times its initial resonance frequency $ω_{0}$ . The value of $' x'$ is [2023]

1 $\frac{1}{4}$

2 $4$

3 $16$

4 $\frac{1}{16}$

Ans.
(1)

$ω = \frac{1}{\sqrt{L C}}$

$\frac{ω}{ω_{0}} = \sqrt{\frac{L C}{8 L \cdot 2 C}} = \frac{1}{4}$

$ω = \frac{ω_{0}}{4}$

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