In a purely capacitive circuit, is it true that the average power is zero?

In a purely capacitive circuit, the average power is indeed zero. This is because, in such circuits, the current and voltage are out of phase by 90 degrees. When the voltage is at its peak, the current is at zero, and when the current is at its peak, the voltage drops back to zero. This phase difference means that although energy is alternately stored in the capacitor and released back into the circuit, there is no net transfer of energy over time; it simply oscillates back and forth.

The average power in an AC circuit is calculated using the formula ( P = VI \cos(\phi) ), where ( \phi ) is the phase angle between the current and voltage. In a purely capacitive circuit, ( \phi ) is 90 degrees, and ( \cos(90°) = 0). This leads to an average power of zero, as the energy is not being consumed but rather just passing through the capacitor.

Understanding this principle is essential because it illustrates the nature of reactive components in AC circuits, where true power (or real power) is only delivered to loads that dissipate energy, such as resistors.