Question

The instantaneous emf and current equations of an a.c. circuit are respectively $e=200\sin (\omega t+\frac{\pi }{3})$ and $i=10\sin \omega t$. The average power consumed over one complete cycle is :

• A. $2000W$
• B. $1000W$
• C. $500W$
• D. $707W$

Answer 1

The correct option is C $500W$

Phase difference between current and emf, $\varphi =\pi /3$

From the given equations, we get peak value o voltage, $V_o=200$ volts

Also peak value of current, $i_o=10A$

Average power consumed, $P_{avg}=\frac{V_o{i}_o}{2}\cos \varphi$

$\therefore$ $P_{avg}=\frac{200\times 10}{2}\cos \frac{\pi }{3}=\frac{200\times 10}{2}\times 0.5$

$⟹$ $P_{avg}=500$ $W$