Question

The current and voltage in an AC circuit are respectively given by $I=I_0\sin \omega t,V=V_0\sin \omega t$ . The power consumed in the circuit is :

• A. $V_0{I}_0$
• B. $\frac{V_0{I}_0}{2}$
• C. $\frac{V_0{I}_0}{\sqrt{2}}$
• D. Zero

Answer 1

Answer: (B)

$\frac{V_0{I}_0}{2}$

The power consumed in the circuit is given as,

$P=V_{rms}{I}_{rms}\cos \varphi$

$=\frac{V_0}{\sqrt{2}}\frac{I_0}{\sqrt{2}}\cos 0^{\circ }$

$=\frac{V_0{I}_0}{2}$

Thus, the power consumed in the circuit is $\frac{V_0{I}_0}{2}$.