The instantaneous values of alternating current and voltages in a circuit are I= 3 2 (200 t) ampere and V = 3 2 (200 t+ 6 ) volt. What is the average power consumed in the circuit in watt?

Step-by-step solution

The given expressions for current and voltage are I = 3 2 (200 t) and V = 3 2 (200 t + 6 ) . The peak current is I₀ = 3 2 A and the peak voltage is V₀ = 3 2 V. The root mean square values are I_ rms = I₀ 2 = 3 2 2 = 3 2 A and V_ rms = V₀ 2 = 3 2 2 = 3 2 V. The phase difference between voltage and current is = 6 . The average power consumed in an AC circuit is given by P_ avg = V_ rms I_ rms . Substituting the values, P_ avg = ( 3 2 ) ( 3 2 ) ( 6 ) . P_ avg = 9 4 3 2 = 9 3 8 W. Answer: 9 3 8