Electro Magnetic Induction And Alternating Currents Question 77

Question: The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by $ V=5\cos \omega t $ volts and I = 2 sin wt amperes (where w = 2pf). The power dissipated in the instrument is [CPMT 1977, 80; MP PET 1999]

Options:

A) Zero

B) 10 W

C) 5 W

D) 2.5 W

Show Answer

Answer:

Correct Answer: A

Solution:

$ V=5\cos \omega t=5\sin ( \omega t+\frac{\pi }{2} ) $
and $ i=2\sin \omega t $ Power $ ={V_{r.m.s.}}\times {i_{r.m.s.}}\times \cos \varphi $ = 0
(Since $ \varphi =\frac{\pi }{2} $ , therefore $ \cos \varphi =\cos \frac{\pi }{2}=0 $ )



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