Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In a series L-C-R circuit, the average power dissipated is half of the maximum power at the frequencies where the phase angle between current and voltage is 4 or - 4 . Reason (R): At half-power frequencies, the numerical value of the net reactance of the circuit is equal to its resistance. In the l

Step-by-step solution

At half-power frequencies, the current amplitude is 1 2 of its maximum value. This occurs when the impedance Z = 2 R . Since Z = R^2 + (X_L - X_C)^2 , we get (X_L - X_C)^2 = R^2 , which implies |X_L - X_C| = R . Thus, the numerical value of the net reactance equals the resistance. Therefore, Reason (R) is true. The phase angle is given by = X_L - X_C R . Since |X_L - X_C| = R , we have = 1 , which gives = 4 . At this phase angle, the power factor is = 1 2 , and the average power is half of the maximum power. Theref