The equation of current in an ac circuit is `I = 4 sin (100pit + pi//6)` ampere. The current at the beginning (t = 0) will be –

Options

A. `1 A`
B. `2A`
C. `3A`
D. `4A`

Answer

To find the current at the beginning (t = 0) in the given AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given equation**:
The equation for the current in the AC circuit is given as:
\[ I = 4 \sin(100 \pi t + \frac{\pi}{6}) \text{ ampere} \]

2. **Substitute t = 0 into the equation**:
To find the current at the beginning (t = 0), we substitute \( t = 0 \) into the equation:
\[ I = 4 \sin(100 \pi \cdot 0 + \frac{\pi}{6}) \]

3. **Simplify the equation**:
This simplifies to:
\[ I = 4 \sin(0 + \frac{\pi}{6}) = 4 \sin\left(\frac{\pi}{6}\right) \]

4. **Calculate \(\sin\left(\frac{\pi}{6}\right)\)**:
We know that:
\[ \sin\left(\frac{\pi}{6}\right) = \sin(30^\circ) = \frac{1}{2} \]

5. **Substitute back to find I**:
Now substitute this value back into the equation:
\[ I = 4 \cdot \frac{1}{2} = 2 \text{ ampere} \]

6. **Conclusion**:
Therefore, the current at the beginning (t = 0) is:
\[ I = 2 \text{ ampere} \]

### Final Answer:
The current at the beginning (t = 0) will be **2 ampere**.

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