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

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 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.

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Excellent

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