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

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 ω 0 ​ . The value of x is:

TestHub · Accepted Answer

Resonance frequency of an LC oscillations circuit is stated as

$ω_{0} = \frac{1}{L C}$ , here, $L an d C$ 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 $ω = \frac{1}{2 L \times 8 C} = \frac{1}{4 L C}$

$\Rightarrow ω = \frac{ω _{0}}{4}$

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

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