For AC voltage applied to a capacitor, the current is ahead of voltage by

Options

A. `pi//2`
B. `pi//4`
C. `(3pi)/4`
D. `pi`

Answer

To solve the question regarding the phase relationship between current and voltage in a capacitor when an AC voltage is applied, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circuit**:
- In an AC circuit with a capacitor, the current and voltage are not in phase. This means that they do not reach their maximum and minimum values at the same time.

**Hint**: Remember that in circuits with reactive components (like capacitors and inductors), the phase relationship between current and voltage is crucial.

2. **Identify the Phase Shift**:
- For a capacitor, the current leads the voltage. This is a key characteristic of capacitive circuits.

**Hint**: Recall that in capacitive circuits, the current reaches its peak before the voltage does.

3. **Use the Formula for Current**:
- The relationship can be expressed mathematically. For a capacitor, the current (I) can be expressed as:
\[ I = I_0 \sin(\omega t + \frac{\pi}{2}) \]
- Here, \(I_0\) is the maximum current, \(\omega\) is the angular frequency, and \(\frac{\pi}{2}\) indicates that the current is leading the voltage.

**Hint**: The sine function indicates that the current is shifted by \(\frac{\pi}{2}\) radians (or 90 degrees) ahead of the voltage.

4. **Conclusion**:
- Since the current leads the voltage by \(\frac{\pi}{2}\) radians, we can conclude that the current is ahead of the voltage by 90 degrees.

**Hint**: Always check the standard phase relationships for capacitors and inductors in AC circuits to avoid confusion.

### Final Answer:
The current is ahead of the voltage by \(\frac{\pi}{2}\) radians (or 90 degrees).