When a dc voltage of 100 V is applied to an inductor, a dc current of 5 A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be 20√3 Ω. The power dissipated in the circuit i s _________ W.
Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit
JEE Mains 2024 06 Apr Morning Shift

Question

When a dc voltage of 100 V is applied to an inductor, a dc current of 5 A flows through it. When an ac voltage of 200 V peak value is connected to inductor, its inductive reactance is found to be 20√3 Ω. The power dissipated in the circuit i s _________ W.

Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit

JEE Mains 2024 06 Apr Morning Shift

G1 Physics · Accepted Answer

For DC: R = V/I = 100/5 = 20 Ω For AC: X(L) = 20√3 Ω Impedance: Z = √[R² + X(L)²] = √[20² + (20√3)²] = √1600 = 40 Ω Peak voltage is 200 V, so: V(rms) = 200/√2 V Current: I(rms) = V(rms)/Z Power dissipated: P = I(rms)²R = (200/(√2 × 40))² × 20 = 250 W