Question

Voltage and current in an ac circuit are given by $V=5\sin (100\pi t-\frac{\pi }{6})$ and $I=4\sin (100\pi t+\frac{\pi }{6})$.

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

Answer 1

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

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

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

So, current leading voltage by $\frac{\pi }{6}-(-\frac{\pi }{6})$

$=\frac{\pi }{3}={60}^0.$