Question

A choke coil takes a current of 2 A lagging 60° behind the applied voltage of 200 V at 50 Hz. Calculate the inductance, resistance and impedance of the coil. Also, determine the power consumed when it is connected across 100-V, 25-Hz supply

Answer 1

(i) Z_coil = 200/2 = 100 Ω; R = Z cos φ = - 100 cos 60° = 50 Ω 

X_L = Z sinφ = 100 sin 60° = 86.6 Ω X_L = 2 π fL = 86.6 

∴ L = 86.6/2π × 50 = 0.275 H 

(ii) Now, the coil will have different impedance because the supply frequency is different but its resistance would remain the same i.e. 50 Ω. Since the frequency has been halved, the inductive reactance of the coil is also halved i.e. it becomes 86.6/2 = 43.3 Ω.

Z_coil = √(50² + 43.3²) = 66.1Ω

I = 100/66.1 = 1.5 A, p.f. = cos φ = 50/66.1 = 0.75 

Power consumed by the coil = VI cos φ = 100 × 1.5 × 0.75 = 112.5W