Both the answers from "Big D" and "N9KXF" are correct, but not complete. There is one aspect that needs to be remembered for AC power - the phase relationship between the voltage and current.
For AC power, the more complete equation for power is P = V * I * cosx, where x is the phase angle between voltage and current.
If the phase angle between voltage and current is 90 degrees, then even though current may be flowing, the total power over a cycle would be zero. Reactive elements like inductors and capacitors have a 90degree phase relationship between voltage and current. They do not "dissipate" energy. They store energy and give it back during different parts of the AC cycle.