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Prove that an...

Question

Prove that an ideal inductor does not dissipate power in an a.c. circuit.

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Solution

The instantaneous EMF is given by E= $E_{o}$ Sin $ω$ t
the instantaneous current in the inductor is given by I= $I_{o}$ cos $ω$ t
the instantaneous power in the inductor is given by P=EI
= $E_{o}$ $I_{o}$ $c o s ω$ tsin $ω$ t
= $\frac{E_{o} I_{o} s i n 2 ω t}{2}$
the average power over the complete cycle $P a v$ = $\frac{E_{o} I_{o} s i n 2 ω t}{2}$ =0
hence,an ideal inductor does not dissipate power

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