In an ac circuit `l=100 sin 200 pi t` . The time required for the current to achieve its peak value will be

Options

A. `1/100 `sec
B. `1/200`sec
C. `1/300`sec
D. `1/400`sec

Answer

To find the time required for the current in the AC circuit described by the equation \( i = 100 \sin(200 \pi t) \) to achieve its peak value, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Peak Value**:
The peak value of the current \( i \) is given as \( i_0 = 100 \). The sine function reaches its maximum value of 1 at specific angles.

2. **Set Up the Equation**:
To find the time when the current reaches its peak value, we need to set the sine function equal to 1:
\[ \sin(200 \pi t) = 1 \]

3. **Determine the Angle**:
The sine function equals 1 at \( \frac{\pi}{2} \) radians (or 90 degrees). Therefore, we can write:
\[ 200 \pi t = \frac{\pi}{2} \]

4. **Solve for Time \( t \)**:
Now, we can solve for \( t \):
\[ t = \frac{\frac{\pi}{2}}{200 \pi} \]
Simplifying this gives:
\[ t = \frac{1}{400} \text{ seconds} \]

5. **Conclusion**:
The time required for the current to achieve its peak value is \( t = \frac{1}{400} \) seconds.

### Final Answer:
The time required for the current to achieve its peak value is \( \frac{1}{400} \) seconds.

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