When a practical coil is connected to a DC source of 100 V , it draws a steady current of 10 A . This coil is then connected in series with a capacitor of capacitance 1000 F across an AC source of RMS voltage 100 V and angular frequency 100 rad s ⁻¹ . If the RMS current in the AC circuit is 5 2 A and the circuit is inductive in nature, the inductance of the coil is _____ mH .

Step-by-step solution

A practical coil consists of an inductance L and an internal resistance R in series. When connected to a DC source, the inductor acts as a short circuit in the steady state. The resistance of the coil is: R = V_ DC I_ DC = 100 10 = 10 When connected to the AC source, the total impedance of the series circuit is: Z = V_ rms I_ rms = 100 5 2 = 10 2 The capacitive reactance is: X_C = 1 C = 1 100 1000 10⁻⁶ = 10 The impedance of the series LCR circuit is given by: Z^2 = R^2 + (X_L - X_C)^2 (10 2 )^2 = (10)^2 + (X_L - 10