Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In a series LCR circuit connected to an AC source, decreasing the capacitance will always result in a decrease in the rms current. Reason (R): Decreasing the capacitance increases the capacitive reactance, which decreases the net impedance if the circuit is initially inductive ( X_L > X_C ). In the

Step-by-step solution

The capacitive reactance is given by X_C = 1 C . When the capacitance C is decreased, the capacitive reactance X_C increases. The net impedance of a series LCR circuit is Z = R^2 + (X_L - X_C)^2 . If the circuit is initially inductive ( X_L > X_C ), an increase in X_C will reduce the magnitude of the difference (X_L - X_C) . This causes the net impedance Z to decrease. Since the rms current is I_ rms = V_ rms Z , a decrease in the impedance Z leads to an increase in the rms current. Therefore, decreasing the capaci