Question

Voltage and current in an AC circuit are given by $V=5\sin (100\pi t-\frac{\pi }{6})$ and $I=4\sin (100\pi t+\frac{\pi }{6})$ respectively. Then, we can conclude -

• A. Voltage leads the current by ${30}^{\circ }$
• B. Current leads the voltage by ${30}^{\circ }$
• C. Current leads the voltage by ${60}^{\circ }$
• D. Voltage leads the current by ${60}^{\circ }$

Answer 1

The correct option is C Current leads the voltage by ${60}^{\circ }$

Given:

$V=5\sin (100\pi t-\frac{\pi }{6})$
$I=4\sin (100\pi t+\frac{\pi }{6})$

The phase difference is,

$\Delta \varphi ={\varphi }_I-{\varphi }_V=(100\pi t+\frac{\pi }{6})-(100\pi t-\frac{\pi }{6})$

$\Rightarrow \Delta \varphi =\frac{\pi }{3}={60}^{\circ }$

$\Rightarrow$ Current leads voltage by ${60}^{\circ }$.

Hence, option $\left(C\right)$ is the correct answer.