inductor L and assume they have been connected for Consider a circuit consisting of a sinusoidal source V s (t) = cos (t) u (t) volts connected in series to a resistor R and an a very long time.
The average power used by the resistor is what you pay to the electric company, but there is also reactive power for which you do not. The complex power supplied to the circuit is defined as:
P = ½ 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.