Q 12-07-153NEETNEET 2022Top questionEasy
A series LCR circuit with inductance $10$ H, capacitance $10\ \mu$F, resistance $50\ \Omega$ is connected to an ac source of voltage, $V = 200\sin(100t)$ volt. If the resonant frequency of the LCR circuit is $\nu_0$ and the frequency of the ac source is $\nu$, then
Answer: (C) $\nu_0 = \nu = \dfrac{50}{\pi}$ Hz
Resonance: $\omega_0 = \dfrac{1}{\sqrt{LC}} = \dfrac{1}{\sqrt{10 \times 10 \times 10^{-6}}} = \dfrac{1}{10^{-2}} = 100$ rad/s, so $\nu_0 = \dfrac{100}{2\pi} = \dfrac{50}{\pi}$ Hz.
Source: $\omega = 100$ rad/s, so $\nu = \dfrac{50}{\pi}$ Hz as well.
Solution by Sreeraj P, M.Sc Physics