Q 12-07-097JEE MainJEE Main 2022 (25 Jun, Shift 2)Medium
In a series LCR circuit, the inductance, capacitance and resistance are $L = 100\ \text{mH}$, $C = 100\ \mu\text{F}$ and $R = 10\ \Omega$ respectively. They are connected to an AC source of voltage $220\ \text{V}$ and frequency of $50\ \text{Hz}$. The approximate value of current in the circuit will be ______ A.
Numerical value type. Enter your answer.
Answer: 22
$X_L = 2\pi\times50\times0.1 = 31.4\ \Omega$; $X_C = \dfrac{1}{2\pi\times50\times10^{-4}} = 31.8\ \Omega$.
$$Z = \sqrt{10^2 + (31.8 - 31.4)^2}\approx10\ \Omega,\qquad I = \frac{220}{10} = 22\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics