In a series LCR circuit, the inductance is 200 mH and the resistance is 20 . The circuit is connected to an AC source of voltage 200 V and frequency 50 Hz . If the RMS current in the circuit is 10 A , the value of capacitance is _____ F .

Step-by-step solution

The RMS current in the circuit is given by I_ rms = V_ rms Z . Therefore, the impedance of the circuit is Z = 200 10 = 20 . Since the impedance Z is equal to the resistance R = 20 , the circuit must be in a state of resonance. This implies that the inductive reactance equals the capacitive reactance ( X_L = X_C ). The angular frequency of the AC source is = 2 f = 2 ( 50 ) = 100 rad s ⁻¹ . The inductive reactance is X_L = L = 100 (200 10⁻³ ) = 20 . Equating X_C to X_L , we get: X_C = 1 C = 20 C = 1 20 100 = 1 2000 F