In a LCR circuit capacitance is changed from $C$ to $2 C$. For the resonant frequency to remain unchanged,…
In a LCR circuit capacitance is changed from $C$ to $2 C$. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to
$4 \mathrm{~L}$
$2 \mathrm{~L}$
L/2
L/4
Solution
$
\omega_{\text {res }}=\frac{1}{\sqrt{L C}}
$
if $\omega_{\text {res }}$ is to remain same, the product LC should also not change.
$
\begin{aligned}
& \Rightarrow \mathrm{LC}=\mathrm{L}^{\prime} \mathrm{C}^{\prime} \\
& \Rightarrow \mathrm{LC}=\mathrm{L}^{\prime} 2 \mathrm{C} \\
& \Rightarrow \mathrm{L}^{\prime}=\mathrm{L}^2 2
\end{aligned}
$