Is the average power in a purely inductive circuit zero?

In a purely inductive circuit, the average power is indeed zero. This is because the current and voltage are out of phase by 90 degrees. In an inductive circuit, when the voltage reaches its maximum, the current is at zero, and when the current reaches its maximum, the voltage is again at zero. This phase difference results in the power factor being zero, so the average power, calculated as the product of voltage, current, and the cosine of the phase angle (which is zero in this case), amounts to zero.

In practical terms, while an inductor can store energy temporarily in its magnetic field, it does not dissipate energy as heat or work, which is typically what is meant by power consumption. Thus, the energy is alternately stored and released, leading to a net average power of zero over one complete cycle of the AC waveform.

The other options do not accurately reflect this characteristic of a purely inductive load: the average power does not depend on frequency in this context, nor is it relevant to voltage levels in a purely inductive situation as it always remains zero regardless of system conditions.