Consider a circuit consisting of a sinusoidal source v_s(t) = cos(t) u(t) connected in series to a resistor Rand an inductor L and assume they have been connected for a very long time.

(a) Let R = 0, L = 1 H, compute the instantaneous and the average powers delivered to the inductor.

(b) Let R = 1Ω ­and L = 1 H, compute the instantaneous and the average powers delivered to the resistor and the inductor.

(c) Let R = 1Ω ­and L = 0 H, compute the instantaneous and the average powers delivered to the resistor.

(d) The complex power supplied to the circuit is defined as P = 1/2 V_s I^∗ where V_s and I are the phasors corresponding to the source and the current in the circuit, and I^* is the complex conjugate of I. Consider the values of the resistor and the inductor given above, and compute the complex power and relate it to the average power computed in each case.