Prove that an ideal inductor does not dissipate power in an a .c circuit.
Let us consider the e.m.f. of the AC signal of the form
Since in the inductor current lags behind e.m.f. therefore current I at an instant is given by
Thus power through an inductor at an instant of time
Now average power in a complete cycle
Thus average power dissipated in an ideal inductor is zero over a full AC cycle
Average Power in an AC Circuit
The instantaneous power at any one moment is the same as in a DC circuit - Joules Law
The average power is the time average of the power over one period.
For a current driven circuit we can rewrite this as,
This equations can be applied to any of the components in an RLC circuit or the oscillator driving the circuit.
Inductor: f = p/2 and cos(p/2) = 0
Thus an ideal inductor can not dissipate any energy, it can only store energy.