Question

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

• 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 $60^{\circ}$

Hint:

If $\phi_I>\phi_V$, current leads voltage.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Phase difference = $\phi_I - \phi_V$.
Step 2: Detailed Explanation:
Phase difference = $\frac{\pi}{6} - \left(-\frac{\pi}{6}\right) = \frac{\pi}{3} = 60^{\circ}$. Since current phase is greater, current leads voltage by $60^{\circ}$.
Step 3: Final Answer:
Current leads voltage by $60^{\circ}$.