Question

In an $L-C-R$ circuit the capacitance is changed from $C$ to $4C$. For the same resonant frequency, the inductance should be changed from $L$ to

• A. L/4
• B. L/2
• C. 2L
• D. 4L

Answer 1

The correct option is A L/4

$\omega =\frac{1}{\sqrt{LC}}$
For, $\omega =constant$ $\to \sqrt{LC}=constant$
Therefore, $C$ is inversely proportional to $L$
So, if $C$ is made $4C$ then $L$ should be reduced to $L/4$ to keep $\omega$ constant.