Q 12-07-127JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
Find the peak current and resonant frequency of the following circuit (as shown in figure).
Answer: (D) $0.2$ A and $50$ Hz
At the source frequency $\omega = 100$ rad s$^{-1}$:
$X_L = \omega L = 100\times0.1 = 10\ \Omega$, $X_C = \dfrac{1}{\omega C} = \dfrac{1}{100\times10^{-4}} = 100\ \Omega$.
$$Z = \sqrt{120^2 + (100-10)^2} = 150\ \Omega,\quad I_0 = \frac{30}{150} = 0.2\ \text{A}$$
Resonant frequency:
$$f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{0.1\times10^{-4}}} = \frac{316}{2\pi} \approx 50\ \text{Hz}$$
Solution by Sreeraj P, M.Sc Physics