A series LCR circuit with R $=20 \Omega, \mathrm{~L}=1.6 \mathrm{H}$ and $\mathrm{C}=40 \mu \mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ______ $\Omega$.

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Alternating Current

A series LCR circuit with R

= 20Ω, L = 1.6 H

and

C = 40 μ F

is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ______

Ω

Answer: 200

At resonance the inductive and capacitive reactances are equal and the angular frequency is

ω_{0} = \frac{1}{L C}

. With

L = 1.6 H

and

C = 40 μ F

ω_{0} = \frac{1}{1.6 \times 40 \times 1 0 ^{- 6}} = \frac{1}{64 \times 1 0 ^{- 6}} = 125 rad/s

. The inductive reactance at this frequency is

X_{L} = ω_{0} L = 125 \times 1.6 = 200 Ω

. The inductive reactance at the resonant frequency is

200 Ω

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Integer answer