I too am kind of confused about what the OP is asking, but I thought I’d muddy the waters just a bit more by talking about apparent power and reactive power and all that.

See, the equation P=VI only works on instantaneous values of V and I, and it only provides the instantaneous power. Often when discussing sinusoidal AC systems, we are more interested in average power delivered to a load, in which case there are 3 different kinds.

There is apparent power, S = VI*, where V and I in this case are complex quantities called phasors which have both a magnitude (the RMS value in the case of V and I) and a phase, and the star denotes the complex conjugate. {See, every sine wave has a magnitude and a phase shift (measured in degrees or radians) from some reference phase. We usually assign the voltage at one point in the circuit a phase of 0, and measure the phases of the other voltages and currents relative to that. Complex cojugation in this case is simply a matter of negating the phase (+30 degrees becomes -30, for instance).} Apparent power is measured in Volt-Amperes, or VA.

There is real power that we are used to, P = VIcos(theta) where theta is the phase difference between V and I. The cos(theta) part goes by the name of “power factor”, and takes on values between 0 and 1. Since the power company can only charge you for real power, they like the power factor to be as close to 1 as possible. Real power is measured in Watts, W.

Finally, there is reactive power, Q = VIsin(theta), measured in Volt-Amps-Reactive, or Var. This is the part of the apparent power that does no work. It is produced as a consequence of the inductance or capacitance of the load. If Q is positive, it is inductive, if negative, it is capacitive. Capacitive (negative) Q flows out of the load rather than into it.

Apparent power, also called complex power, is the sum of the real and reactive power, S = P +jQ, where j is the imaginary unit.

Anyway, I may have written too much, but the point is that when we look at average power in AC systems, things become a lot more complicated than p=vi. The complications arise because of the reactive impedance in the circuit. If the circuit is purely resistive, then there are no phase shifts, Q becomes zero, and P = S = VI. This is another reason why the power company likes a power factor of 1.