Question

In an AC circuit, V and i are given by V = 100 sin (100t) volt and i = 100 sin $\bigg( 100 t + \frac{ \pi}{ 3} \bigg)$ amp .The power dissipated in the circuit is

• A. $10^4$W
• B. 2.5 W
• C. 5 k W
• D. 10 W

Answer 1

Answer: (B)

2.5 W

Answer 2

Here, $V_0 = 100\,V, \, i_0 = 100 \,A$ and phase difference
$\phi = \frac{ \pi}{ 3}$
$\therefore p = V_{ rms} \times i_ { rms} \times cos \, \phi$
= $\frac{ V_0 i_0}{ 2 } cos \, \phi = \frac{ 100 \times 100 }{ 2} \times \frac{ 1}{ 2}$

= 2500W = 2.5 k W