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 :
Solution
The resonance frequency of LC oscillations circuit is<br/><br/>
$$
\begin{aligned}
& \omega_0=\frac{1}{\sqrt{\mathrm{LC}}} \\\\
& \mathrm{L} \rightarrow 2 \mathrm{~L} \\\\
& \mathrm{C} \rightarrow 8 \mathrm{C} \\\\
& \omega=\frac{1}{\sqrt{2 \mathrm{~L} \times 8 \mathrm{C}}}=\frac{1}{4 \sqrt{\mathrm{LC}}} \\\\
& \omega=\frac{\omega_0}{4}
\end{aligned}
$$<br/><br/>
So $\mathrm{x}=\frac{1}{4}$
About this question
Subject: Physics · Chapter: Alternating Current · Topic: AC Circuits: R, L, C
This question is part of PrepWiser's free JEE Main question bank. 115 more solved questions on Alternating Current are available — start with the harder ones if your accuracy is >70%.