Q 12-07-090JEE MainJEE Main 2023 (1 Feb, Shift 1)Easy
A series LCR circuit is connected to an ac source of $220$ V, $50$ Hz. The circuit contains a resistance $R=100\ \Omega$ and an inductor of inductive reactance $X_L=79.6\ \Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $\mu$F.
Numerical value type. Enter your answer.
Answer: 40
Maximum power at resonance: $X_C=X_L$, so $C=\dfrac{1}{2\pi fX_L}=\dfrac{1}{314\times79.6}\approx4.0\times10^{-5}$ F $=40\ \mu$F.
Solution by Sreeraj P, M.Sc Physics