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 $\omega_0$ The value of $x$ is:

• A. $1 / 4$
• B. 4
• C. 16
• D. 1/16

Answer 1

The Correct Option is A

1. The resonant frequency of an LC circuit is given by: \[ \omega_0 = \frac{1}{\sqrt{LC}}. \] 
2. When \(L \to 2L\) and \(C \to 8C\), the new resonant frequency is: \[ \omega = \frac{1}{\sqrt{2L \cdot 8C}} = \frac{1}{\sqrt{16LC}} = \frac{1}{4} \omega_0. \] 
Thus, the value of \(x\) is \(1/4\). 

The resonant frequency of an LC oscillator decreases as the inductance and capacitance increase, since \(\omega_0 \propto 1/\sqrt{LC}\).