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 $ .
