In an AC circuit, the instantaneous values of emf and current are $ξ= 100 \sin (314t) V$ and $I = \sin(314t+ π/3) A$. The average power consumed in the circuit is

25 W

The correct answer is Option (4) → 25 W

Given:

$\xi = 100\sin(314t)\,V$, $I = \sin(314t + \frac{\pi}{3})\,A$

Formula:

Average power, $P = E_{rms} \, I_{rms} \cos\phi$

From equations:

Phase difference, $\phi = \frac{\pi}{3}$

$E_0 = 100\,V$

$E_{rms} = \frac{E_0}{\sqrt{2}} = \frac{100}{\sqrt{2}}$

$I_0 = 1\,A$

$I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{1}{\sqrt{2}}$

Substitute values:

$P = \frac{100}{\sqrt{2}} \times \frac{1}{\sqrt{2}} \times \cos\frac{\pi}{3}$

$P = 50 \times \frac{1}{2}$

$P = 25\,W$

Final Answer:Average power = 25 W