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