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

The problem provides us with the voltage and current expressions in an AC circuit:

• Voltage: \(V = 5\sin\left(100\pi t - \frac{\pi}{6}\right)\)
• Current: \(I = 4\sin\left(100\pi t + \frac{\pi}{6}\right)\)

To determine which waveform leads the other, we need to compare the phase angles in the expressions.

Steps to solution:

1. Identify the phase angles from the given trigonometric expressions:
   • The phase of the voltage: \(\phi_V = -\frac{\pi}{6}\)
   • The phase of the current: \(\phi_I = \frac{\pi}{6}\)
2. Calculate the phase difference between voltage and current:
3. Convert the phase difference from radians to degrees:
4. Interpret the result:
   • The positive phase difference \(60^\circ\) indicates that the current leads the voltage by \(60^\circ\).

Conclusion: The correct answer is that the current leads the voltage by \(60^{\circ}\).