Q.What is meant by a wattless current? Explain why the current flowing in a purely inductive or a purely capacitive AC circuit consumes no power on average even though a genuine current is flowing through it.

Definition. A wattless current is the component of current that is exactly $90^\circ$ out of phase with the applied voltage, and therefore delivers zero average power however large its rms magnitude is -- exactly the situation in a purely inductive or purely capacitive AC circuit.

Why the power genuinely averages to zero. With $i$ exactly $90^\circ$ out of phase with $v$, the instantaneous power $p=vi$ is positive during one quarter of every cycle (energy genuinely flowing FROM the source INTO the inductor's magnetic field, or the capacitor's electric field) and negative during the next quarter (that same energy flowing back OUT, returning to the source). Over a whole cycle, these positive and negative contributions cancel exactly, so no NET energy is transferred, even though the instantaneous power is nonzero at almost every moment along the way and a genuine current is clearly flowing (heating any real resistance in the wires as it does so). …

Explain the phase condition that defines a wattless current, then trace the instantaneous power's alternating sign …

• Claiming a wattless current 'does nothing' -- it is a real current and does heat resistive components even though it delivers no net power to the load. …