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 ω 0 . The value of x is:

Question

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 &#969; 0 . The value of x is:

Aicharya · Accepted Answer

Resonance frequency of an LC oscillations circuit is stated as

$ω_{0} = \frac{1}{\sqrt{L C}}$ , here, $L and C$ represents inductance and capacitance of circuit.

Now, when inductance and capacitance changes, i.e., $L^{'} = 2 L$ and $C^{'} = 8 C$

Then, resonant frequency is $ω = \frac{1}{\sqrt{2 L \times 8 C}} = \frac{1}{4 \sqrt{L C}}$

$\Rightarrow ω = \frac{ω_{0}}{4}$

Thus, the value of $x = \frac{1}{4}$ .

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively,…

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