SSE JE Electrical Engineering 29 Oct 2020 Shift 2 Papers

The circuit which contains only inductance (L) and not any other quantities like resistance and capacitance in the circuit is called a purely inductive circuit.
In this type of circuit, the current lags the voltage by an angle of 90 degrees.
The Circuit containing pure inductance is shown below.
The waveform, power curve and phasor diagram of a purely inductive circuit is shown belowInstantaneous power in the inductive circuit is given by, P = VI
$\mathrm{P}=\left({\mathrm{V}}_{\mathrm{m}}\sin \mathrm{\omega }\mathrm{t}\right).\left({\mathrm{I}}_{\mathrm{m}}\sin \left(\mathrm{\omega }\mathit{t}+\frac{\mathrm{\pi }}{2}\right)\right)$
$={\mathrm{V}}_{\mathrm{m}}{\mathrm{I}}_{\mathrm{m}}\sin \mathrm{\omega }\mathit{t}\cos \mathrm{\omega }\mathrm{t}$
$=\frac{{\mathrm{V}}_{\mathrm{m}}{\mathrm{I}}_{\mathrm{m}}}{2}2\sin \mathrm{\omega }\mathrm{t}\cos \mathrm{\omega }\mathrm{t}$
$=\frac{{\mathrm{V}}_{\mathrm{m}}{\mathrm{I}}_{\mathrm{m}}}{2}\sin 2\mathrm{\omega }\mathrm{t}=0$
Hence, the average power consumed in a purely inductive circuit is zero.