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 0. The value of x is:
Select the correct option:
A
1/4
B
16
C
1/16
D
4
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. The resonance frequency of LC oscillations circuit is
$$
\begin{aligned}
& \omega_0=\frac{1}{\sqrt{L C}} \\
& \mathrm{~L} \rightarrow 2 \mathrm{~L} \\
& \mathrm{C} \rightarrow 8 \mathrm{C}
\end{aligned}
$$
$$
\begin{aligned}
& \omega=\frac{1}{\sqrt{2 L \times 8 C}}=\frac{1}{4 \sqrt{L C}} \\
& \omega=\frac{\omega_0}{4} \\
& x=\frac{1}{4}
\end{aligned}
$$
So,
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