What condition must be fulfilled for an AC circuit to be purely resistive?

For an alternating current (AC) circuit to be purely resistive, a fundamental condition is that the current and voltage must be in phase. This means that both the current and voltage waveforms reach their maximum and minimum values simultaneously, resulting in the absence of any phase difference between them.

In a purely resistive circuit, the power factor is unity (1), meaning that all of the power supplied by the source is being converted into useful work (as heat, light, etc.) without any reactive power due to inductance or capacitance. When resistance is the only component in the circuit, all the energy flows freely without being stored in a magnetic or electric field, which would otherwise cause the current to lag or lead the voltage.

Therefore, having no lagging or leading current directly illustrates that the circuit exhibits purely resistive behavior, where the voltage and current are synchronized, leading to efficient energy utilization.