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
Answer & explanation
Correct answer: option 4
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