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An alternating e.m.f. of angular frequency is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency

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$\frac{\omega }{2}$

2ω

$\frac{\omega }{4}$

answer is D.

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Detailed Solution

The instantaneous values of emf and current in inductive circuit are given by

$E = {E_o}\sin \omega t\,\,and\,\,i = {i_o}\sin \left( {\omega t - \frac{\pi }{2}} \right)\,\,respectively.$

$so,\,\,{P_{inst}} = Ei = {E_0}\sin \omega t \times {i_0}\sin \left( {\omega t - \frac{\pi }{2}} \right)$

$= {E_0}{i_0}\sin \omega t\left( {\sin \omega t\cos \frac{\pi }{2} - \cos \omega t\sin \frac{\pi }{2}} \right)$

$= {E_0}{i_0}\sin \omega t\;\cos \omega t$

$= \frac{1}{2}{E_0}{i_0}\sin 2\omega t$ $(\sin 2\omega t = 2\sin \omega t\;\cos \omega t)$

Hence, angular frequency of instantaneous power is 2ω .

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