Question

In an AC circuit the potential difference V and current I are given respectively by $ V=100\sin (100t)volt $ and $ I=100\sin \left( 100t+\frac{\pi }{3} \right)mA $ The power dissipated in the circuit will be

• A. $ {{10}^{4}}W $
• B. $ 10W $
• C. $ 2.5\text{ }W $
• D. $ 5W $

Answer 1

Answer: (C)

Voltage amplitude $ {{V}_{0}}=100\,V, $ current amplitude $ {{I}_{0}}=100\,mA=100\times {{10}^{-3}}A $ Phase difference $ \phi =\frac{\pi }{3}=60{}^\circ $ Power dissipated $ p=\frac{{{V}_{0}}{{I}_{0}}}{2}\cos \phi $ $ =\frac{100\times 100\times {{10}^{-3}}}{2}\times \cos 60{}^\circ $ $ =2.5\,W $