Question 51:
easyA 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 resonant frequency of the LCR circuit is $\nu_0$ and the frequency of the ac source is $\nu$, then:
(2022)
For the AC source $V = 200 \sin(100t)$, angular frequency $\omega = 100 rad/s$.
Source frequency $\nu = \frac{\omega}{2\pi} = \frac{100}{2\pi} = \frac{50}{\pi} Hz$.
Resonant frequency $\nu_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{10 \times 10 \times 10^{-6}}} = \frac{1}{2\pi\times 10^{-2}} = \frac{50}{\pi} Hz$.
Thus, $\nu_0 = \nu = \frac{50}{\pi} Hz$.