Question

Resonance frequency of a circuit is $f$. If the capacitance is made $4$ times the initial value, then the resonance frequency will become

• A. $\frac{f}{2}$
• B. $2f$
• C. $f$
• D. $\frac{f}{4}$

Answer 1

Answer: (A)

$\frac{f}{2}$

As we know,

Resonance frequency of a circuit
$f=\frac{1}{2\pi \sqrt{LC}}$
ie, $f\propto \frac{1}{\sqrt{C}}$
$\Rightarrow \frac{f^{\prime }}{f}=\frac{\sqrt{C}}{\sqrt{4C}}=\frac{1}{2}$
$\Rightarrow f^{\prime }=\frac{f}{2}$