Electro Magnetic Induction And Alternating Currents Question 135

Question: An alternating e.m.f. of angular frequency $ \omega $ is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency [Roorkee 1999]

Options:

A) $ \frac{\omega }{4} $

B) $ \frac{\omega }{2} $

C) $ \omega $

D) $ 2\omega $

Show Answer

Answer:

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 ( \omega t-\frac{\pi }{2} ) $ respectively.

So, $ P_{inst}=Ei=E_{0}\sin \omega t\times i_{0}\sin ( \omega t-\frac{\pi }{2} ) $

$ =E_{0}i_{0}\sin \omega t( \sin \omega t\cos \frac{\pi }{2}-\cos \omega t\sin \frac{\pi }{2} ) $

$ =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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