Alternating Current Question 3

Question 3 - 25 January - Shift 1

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:

(1) $1 / 4$

(2) 16

(3) $1 / 16$

(4) 4

Show Answer

Answer: (1)

Solution:

Formula: Resonant Frequency

The resonance frequency of LC oscillations circuit is

$\omega_0=\frac{1}{\sqrt{LC}}$

$L \to 2 L$

$C \to 8 C$

$\omega=\frac{1}{\sqrt{2 L \times 8 C}}=\frac{1}{4 \sqrt{LC}}$

$\omega=\frac{\omega_0}{4}$

So $x=\frac{1}{4}$