Determine the power losses equation for pure inductive load.

Power in Pure Inductive Circuit:

Instantaneous power in the inductive circuit is given by 

p = vi

$P=\left(V_m\sin \omega t\right)\left(I_m\sin \left(\omega t+\frac{\mathrm{\pi }}{2}\right)\right)$

$P = V_m{I}_m\sin \omega t \cos \omega t$

$P = \frac{V_m{I}_m}{2} 2 \sin \omega t \cos \omega t$

$P=\frac{V_m}{\sqrt{2}}\frac{i_m}{\sqrt{2}}\sin 2\omega or$

P = 0

Hence, the average power consumed in a purely inductive circuit is zero.

The average power in one alteration, i.e., in a half cycle is zero, as the negative and positive loop is under power curve is the same.

In the purely inductive circuit, during the first quarter cycle, the power supplied by the source, is stored in the magnetic field set up around the coil. In the next quarter cycle, the magnetic field diminishes and the power that was stored in the first quarter cycle is returned to the source. This process continues in every cycle, and thus, no power is consumed in the circuit.