the power consumed in a circuit element will be least when the phase difference between the current and voltage is

The power consumed in a circuit element is least when the phase difference between the current and voltage is 90° (or equivalently 270°). At this phase difference, the power factor cos⁡θ\cos \theta cosθ is zero, meaning no real power is consumed—only reactive power flows in the circuit, resulting in zero net power consumption. This condition typically occurs in purely reactive components like ideal inductors or capacitors where voltage and current are out of phase by 90°.

Explanation

• Power consumed P=VrmsIrmscos⁡θP=V_{rms}I_{rms}\cos \theta P=Vrms​Irms​cosθ, where θ\theta θ is the phase difference between voltage and current.
• When θ=90∘\theta =90^\circ θ=90∘ or 270∘270^\circ 270∘, cos⁡θ=0\cos \theta =0cosθ=0, so the real power consumed is zero.
• Thus, the circuit consumes the least power under these conditions, meaning energy storage elements (inductors or capacitors) exchange reactive power with the source without dissipating real power.

Hence, the least power consumption occurs at a phase difference of 90° between current and voltage.