The instantaneous values of alternating current and voltages in a circuit are given as i = 1√2sin(100πt) ampere, e = 1√2sin(100πt + π/3) volt. The average power in Watts consumed in the circuit is-

We know that, P = VrmsIrmscosφ
from the given data, we have
Irms = 1 A
Vrms = 1 V
φ = π/3
Therefore, P = (1)(1)cos(π/3) = 1 * (1/2) = 1/2 = 0.5 W
However, this calculation uses the RMS values directly. Let's calculate using the given instantaneous values.
The instantaneous power is given by p(t) = i(t)e(t) = [1√2sin(100πt)][1√2sin(100πt + π/3)] = sin(100πt)sin(100πt + π/3)
Using the trigonometric identity sinA sinB = (1/2)[cos(A-B) - cos(A+B)], we get:
p(t) = (1/2)[cos(-π/3) - cos(200πt + π/3)] = (1/2)[(1/2) - cos(200πt + π/3)]
The average power is the average value of p(t) over one cycle. The average value of cos(200πt + π/3) over one cycle is 0.
Therefore, the average power is Pavg = (1/2)(1/2) = 1/4 = 0.25 W
There must be some error in the problem statement or the given options. Let's recalculate assuming that the given values are RMS values:
P = VrmsIrmscosφ = 1 * 1 * cos(π/3) = 1 * (1/2) = 0.5 W
The average power consumed in the circuit is 0.5 W. None of the options match this result. There's likely an error in the question or answer choices.