Given below are two statements: one is labelled as Assertion and the other is labelled as Reason. Assertion: When an AC voltage V = 260 (500 t) V is applied to a series LCR circuit with L = 160 mH, C = 10 , F, and R = 50 , , the peak current in the circuit is 2 A. Reason: In this circuit, the voltage leads the current because the inductive reactance is greater than the capacitive reactance. In the light of the above

Step-by-step solution

From the given equation V = 260 (500 t) V, we have V_m = 260 V and = 500 rad/s. The inductive reactance is X_L = L = 500 160 10⁻³ = 80 , . The capacitive reactance is X_C = 1 C = 1 500 10 10⁻⁶ = 1 5 10⁻³ = 200 , . The impedance is Z = R^2 + (X_L - X_C)^2 = 50^2 + (80 - 200)^2 = 50^2 + (-120)^2 = 130 , . The peak current is I_m = V_m Z = 260 130 = 2 A. Thus, the Assertion is correct. For the Reason: Since X_C (200 , ) > X_L (80 , ) , the circuit is predominantly capacitive. In a capacitive circuit, the current leads