The instantaneous values of alternating current and voltages in a circuit given as aligned & i= 1 2 (100 t) amp & e= 1 2 (100 t+ / 3) volt aligned The average power (in watts) consumed in the circuit is

Step-by-step solution

The instantaneous current is given by i = I₀ ( t) where I₀ = 1 2 A and = 100 rad/s. The instantaneous voltage is given by e = E₀ ( t + ) where E₀ = 1 2 V and = 3 rad. The average power consumed in an AC circuit is given by the formula P_ avg = V_ rms I_ rms ( ) , where V_ rms = E₀ 2 and I_ rms = I₀ 2 . Substituting the given values: V_ rms = 1/ 2 2 = 1 2 V I_ rms = 1/ 2 2 = 1 2 A The phase difference is = 3 , so ( ) = ( 3 ) = 1 2 . Therefore, P_ avg = 1 2 1 2 1 2 = 1 8 W. Answer: 1 8