When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A. The self inductance of the coil i s ______ mH. (Take π = 3)
Physics · Ac Cirucuits · series combination of ac circuit and L-C-R circuit
JEE Mains 2024 09 Apr Morning Shift

Question

When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A. The self inductance of the coil i s ______ mH. (Take π = 3)

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

JEE Mains 2024 09 Apr Morning Shift

G1 Physics · Accepted Answer

For DC: R = V/I = 20/5 = 4 Ω For AC: Z = V/I = 20/4 = 5 Ω For an RL coil: Z² = R² + X(L)² Therefore: X(L) = √(5² - 4²) = 3 Ω Also: X(L) = 2πfL Therefore: L = 3/[2 × 3 × 50] = 0.01 H = 10 mH