Question

An alternating voltage $V=V_0\sin \omega t$ is applied across a circuit. As a result, a current $I=I_0\sin (\omega t-\pi /2)$ flows in it. The power consumed per cycle is

• A. zero
• B. $0.5V_0{I}_0$
• C. $0.707V_0{I}_0$
• D. $1.414V_0{I}_0$

Answer 1

Answer: (A)

In the circuit, voltage $V=V_0\sin \omega t$ and current
$I=T_0\sin \left(\omega t-\frac{\pi }{2}\right)$
Phase different between voltage and current at any time would be
$\varphi =\frac{\pi }{2}$ (from phasor diagram)
So power consumed,
$P=\frac{I_0{V}_0}{2}\cos \varphi$
$=\frac{I_0{V}_0}{2}\cos \left(\frac{\pi }{2}\right)$
$=P=0$