Q 12-07-110JEE MainJEE Main 2022 (28 Jul, Shift 1)Medium
The frequencies at which the current amplitude in an LCR series circuit becomes $\dfrac{1}{\sqrt2}$ times its maximum value, are $212\ \text{rad s}^{-1}$ and $232\ \text{rad s}^{-1}$. The value of resistance in the circuit is $R = 5\ \Omega$. The self inductance in the circuit is ______ mH.
Numerical value type. Enter your answer.
Answer: 250
The half-power frequencies are separated by the bandwidth:
$$\omega_2 - \omega_1 = \frac RL \Rightarrow 232 - 212 = \frac{5}{L}$$
$$L = \frac{5}{20} = 0.25\ \text{H} = 250\ \text{mH}$$
Solution by Sreeraj P, M.Sc Physics