The instantaneous values of current and voltage in an AC circuit are given by
l = 6sin ( 100`pi`t + `pi` / 4)
V = 5sin ( 100 `pi`t - `pi` / 4 ), then

Options

A. current leads the voltage by `45^(@)`
B. voltage leads the current by `90^(@)`
C. current leads the voltage by `90^(@)`
D. voltage leads the current by `45^(@) `

Explanation

To solve the problem, we need to determine the phase difference between the current and voltage in the given AC circuit.

### Step-by-Step Solution:

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

2. **Extract the phase angles:**
- The phase angle for the current \( \phi_I = \frac{\pi}{4} \)
- The phase angle for the voltage \( \phi_V = -\frac{\pi}{4} \)

3. **Calculate the phase difference:**
- The phase difference \( \Delta \phi \) is given by:
\[ \Delta \phi = \phi_I - \phi_V \]
- Substitute the values:
\[ \Delta \phi = \frac{\pi}{4} - \left(-\frac{\pi}{4}\right) = \frac{\pi}{4} + \frac{\pi}{4} = \frac{\pi}{2} \]

4. **Convert the phase difference to degrees:**
- Since \( \frac{\pi}{2} \) radians is equivalent to \( 90^\circ \).

5. **Determine the relationship between current and voltage:**
- Since the phase difference \( \Delta \phi = \frac{\pi}{2} \) indicates that the current leads the voltage, we conclude:
- Current leads the voltage by \( 90^\circ \).

### Final Answer:
Current leads the voltage by \( 90^\circ \).