Electro Magnetic Induction And Alternating Currents Question 78

Question: In an ac circuit, V and I are given by V = 100 sin (100 t) volts, $ I=100\sin ,( 100t+\frac{\pi }{3} ),mA $ . The power dissipated in circuit is [MP PET 1989; RPET 1999; MP PMT 1999, 2002]

Options:

A) 104 watt

B) 10 watt

C) 2.5 watt

D) 5 watt

Show Answer

Answer:

Correct Answer: C

Solution:

$ P={V_{r.m.s.}}\times {i_{r.m.s.}}\times \cos \varphi $

$ =\frac{100}{\sqrt{2}}\times \frac{100\times {{10}^{-3}}}{\sqrt{2}}\times \cos \frac{\pi }{3} $

$ =\frac{10^{4}\times {{10}^{-3}}}{2}\times \frac{1}{2}=\frac{10}{4}=2.5\ watt $



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