A series LCR circuit is connected to an AC source V = 100 2 (1000 t) Volts. The current amplitude in the circuit is 2 A. Given that R = 50 , , L = 100 mH, and the voltage leads the current, the value of capacitance C is :

Step-by-step solution

From the given voltage equation V = 100 2 (1000 t) , the peak voltage is V_m = 100 2 V and the angular frequency is = 1000 rad/s. The impedance of the circuit is given by Z = V_m I_m = 100 2 2 = 50 2 , . Using the impedance formula Z^2 = R^2 + (X_L - X_C)^2 , we have: (50 2 )^2 = 50^2 + (X_L - X_C)^2 5000 = 2500 + (X_L - X_C)^2 (X_L - X_C)^2 = 2500 |X_L - X_C| = 50 , The inductive reactance is X_L = L = 1000 (100 10⁻³) = 100 , . Since the voltage leads the current, the circuit is inductive, which means X_L > X_C .