Voltage and current in an ac circuit are given by
`V=5 sin (100 pi t-pi/6)` and `I=4 sin (100 pi t+pi/6)`

Options

A. voltage leads the current by `30^(@)`
B. current leads the voltage by `30^(@)`
C. current leads the voltage by `60^(@)`
D. voltage leads the current by `60^(@)`

Explanation

To solve the problem, we need to analyze the given voltage and current functions in an AC circuit.

**Step 1: Identify the given voltage and current functions.**
- Voltage: \( V(t) = 5 \sin(100 \pi t - \frac{\pi}{6}) \)
- Current: \( I(t) = 4 \sin(100 \pi t + \frac{\pi}{6}) \)

**Step 2: Determine the phase angles of voltage and current.**
- The phase angle for voltage \( V \) is \( -\frac{\pi}{6} \).
- The phase angle for current \( I \) is \( +\frac{\pi}{6} \).

**Step 3: Calculate the phase difference between current and voltage.**
- The phase difference \( \Delta \phi \) can be calculated as:
\[ \Delta \phi = \phi_I - \phi_V = \left( \frac{\pi}{6} - \left(-\frac{\pi}{6}\right) \right) = \frac{\pi}{6} + \frac{\pi}{6} = \frac{2\pi}{6} = \frac{\pi}{3} \]

**Step 4: Interpret the phase difference.**
- Since the current phase angle is greater than the voltage phase angle, we conclude that the current leads the voltage by \( \frac{\pi}{3} \) radians.

**Step 5: Convert the phase difference to degrees.**
- To convert radians to degrees:
\[ \frac{\pi}{3} \text{ radians} = \frac{\pi}{3} \times \frac{180}{\pi} = 60^\circ \]

**Step 6: Conclusion.**
- Therefore, we conclude that the current leads the voltage by \( 60^\circ \).

**Final Answer:**
Current leads the voltage by \( 60^\circ \).

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