A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains resistance R = 100 Ω and an inductor of inductive reactance X(L) = 79.6 Ω. The capacitance needed to maximize the average rate at which energy is supplied is ______ μF.
Physics · Circular Motion
JEE Mains 1 February 2023 Shift 1 Morning Shift

Question

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains resistance R = 100 Ω and an inductor of inductive reactance X(L) = 79.6 Ω. The capacitance needed to maximize the average rate at which energy is supplied is ______ μF.

Physics · Circular Motion

G1 Physics · Accepted Answer

Average power is maximum at resonance, where X(L)=X(C). Hence 79.6 = 1/(ωC) with ω=2πf=2π×50. Therefore C = 1/[2π×50×79.6] ≈ 40 μF.