A) \[\frac{\omega }{4}\]
B) \[\frac{\omega }{2}\]
C) \[\omega \]
D) \[2\omega \]
Correct Answer: D
Solution :
The instantaneous values of emf and current in inductive circuit are given by \[E={{E}_{0}}\sin \omega t\]and \[i={{i}_{0}}\sin \left( \omega t-\frac{\pi }{2} \right)\]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 \[2\omega \].
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