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. $10\,W$
• C. $2.5\,W$
• D. $5\,W$

Answer 1

Answer: (C)

$2.5\,W$

Answer 2

Voltage amplitude $V_0 = 100 \,V$, current amplitude $i_0 = 100 \, mA = 100 \times 10^{ -3 }\, A$ and phase difference between i and $V$ is $\phi = \frac{ \pi}{ 3} = 60^\circ$ . Now power dissipated is given by P = $\frac{ V_0 \, i_0}{ 2} \, \cos \, \phi$ $= \frac{ 100 \times 100 \times 10^{ - 3} }{ 2} \times \, cos \, 60^\circ$ $= 2.5\, W$