A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain 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 ______ $\mu \mathrm{F}$.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Alternating Current

A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain a resistance

R = 100Ω

and an inductor of inductive reactance

X_{L} = 79.6Ω

. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______

μ F

Answer: 40

The power supplied to a series

L C R

circuit is greatest at resonance, where the capacitive reactance matches the inductive one,

X_{C} = X_{L}

. Thus

\frac{1}{ω C} = 79.6 Ω

with

ω = 2 π (50) rad s^{- 1}

, so

C = \frac{1}{2 π ( 50 ) ( 79.6 )} = 4.0 \times 1 0^{- 5} F = 40 μ F .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer