Question

A series LCR circuit with inductance $10H$, capacitance $10\mu F$, resistance $50\Omega$ is connected to an ac source of voltage, $V=200\sin \left(100t\right)$ volt. If the resonant frequency of the LCR circuit is $v_0$ and the frequency of the ac source is $v$, then

Answer 1

Resonant frequency $2\pi v_0=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{10\times {10}^{-6}\times 10}}$

$2\pi v_0=100$

$v_0=\left(\frac{50}{\pi }\right)\text{Hz}$

$v=200\sin \left(100t\right)$

$100=2\pi v\Rightarrow v=\left(\frac{50}{\pi }\right)\text{Hz}$
Hence, the correct option is $\text{(}d)$.