Question

In an a.c. circuit, V and I are given by V = 100 sin (100t) volt I = 100 sin (100t + $\pi$/3) mA Then the power dissipated in the circuit is

• A. $10^4\,W$
• B. $10\,W$
• C. 2500 W
• D. 5 W

Answer 1

Answer: (C)

2500 W

Answer 2

Considering the given equation for V and I, $E_0$ = 100V, $I_0$ = 100A and $\phi = \frac{\pi}{3}$ then, $E_{r.m.s} = \frac{E_0}{\sqrt{2}} = \frac{100}{\sqrt{2}}$ and $I_{r.m.s.} = \frac{1}{\sqrt{2}} = \frac{100}{\sqrt{2}}$ Now, Power dissipated in the circuit is given by P = $E_{r.m.s} \, I_{r.m.s} \, cos \, \phi$ = $\frac{100}{\sqrt{2}} \times \frac{100}{\sqrt{2}} \times cos \frac{\pi}{3} = \frac{100 \times 100}{2} \times \frac{1}{2}$ = 2500W