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, if the inductive reactance is twice the capacitive reactance ( X_L = 2X_C ) and the resistance equals the capacitive reactance ( R = X_C ), the current lags the source voltage by 45^ . Reason (R): The rms current in a series LCR circuit is maximum when the inductive reactan

Step-by-step solution

For the Assertion (A): The phase angle in a series LCR circuit is given by: = X_L - X_C R Substituting the given values ( X_L = 2X_C and R = X_C ): = 2X_C - X_C X_C = X_C X_C = 1 = 45^ Since X_L > X_C , the circuit is net inductive. In an inductive circuit, the voltage leads the current, meaning the current lags the source voltage by 45^ . Thus, Assertion (A) is true. For the Reason (R): The rms current in a series LCR circuit is I_ rms = V_ rms R^2 + (X_L - X_C)^2 . This current is maximum when X_L = X_C (resonanc