Question

At $42$ $Hz,$ an inductor has impedence $36$ times that of impedence of a capacitor. Find resonance frequency of the circuit.

• A. 4 Hz
• B. 5 Hz
• C. 6 Hz
• D. 7 Hz

Answer 1

The correct option is D 7 Hz

$\begin{array}{c}{X}_L=\omega L\\ X_C=\frac{1}{\omega C}\end{array}\}$
$X_L=36X_C$ at f = 42 Hz.
$2\pi fL=36.\frac{1}{2\pi fC}$
$f^2=\frac{36}{4{\pi }^{2}LC}$
$f=\frac{6}{2\pi \sqrt{LC}}=6\times f_o$
where $f_0=\frac{1}{\sqrt{LC}}$ is the resonance frequency.
$\Rightarrow f_0=\frac{f}{6}=42/6=7Hz$