Question

In a series L.C.R. circuit an alternating emf $\left(v\right)$ and current $\left(i\right)$ are given by the equation $v=v_0\sin \omega t,i=i_0\sin (\omega t+\frac{\pi }{3})$
The average power discipated in the circuit over a cycle of AC is

• A. $\frac{v_0{i}_0}{2}$
• B. $\frac{v_0{i}_0}{4}$
• C. $\frac{\sqrt{3}}{2}{v}_0{i}_0$
• D. Zero

Answer 1

Answer: (B)

$\frac{v_0{i}_0}{4}$

On comparing the current given with: $i=i_o\sin (wt+\varphi )$

We get, $\varphi =\frac{\pi }{3}$

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

$\therefore$ $P_{avg}=\frac{v_o{i}_o}{2}\times \frac{1}{2}=\frac{v_o{i}_o}{4}$ $(\because cos(\pi /3)=1/2)$