For an alternating voltave `V=10 cos 100 pit` volt, the instantenous voltage at `t=1/600`s is

Options

A. `1V`
B. `5V`
C. `5sqrt(3)V`
D. `10V`

Explanation

To find the instantaneous voltage at \( t = \frac{1}{600} \) seconds for the alternating voltage given by the equation \( V(t) = 10 \cos(100 \pi t) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given voltage equation**:
\[ V(t) = 10 \cos(100 \pi t) \]

2. **Substitute the value of \( t \)**:
We need to find \( V \) at \( t = \frac{1}{600} \) seconds. Substitute \( t \) into the equation:
\[ V\left(\frac{1}{600}\right) = 10 \cos\left(100 \pi \cdot \frac{1}{600}\right) \]

3. **Calculate the argument of the cosine**:
\[ 100 \pi \cdot \frac{1}{600} = \frac{100 \pi}{600} = \frac{\pi}{6} \]

4. **Substitute back into the voltage equation**:
Now we substitute \( \frac{\pi}{6} \) back into the equation:
\[ V\left(\frac{1}{600}\right) = 10 \cos\left(\frac{\pi}{6}\right) \]

5. **Find the value of \( \cos\left(\frac{\pi}{6}\right) \)**:
The value of \( \cos\left(\frac{\pi}{6}\right) \) is \( \frac{\sqrt{3}}{2} \):
\[ V\left(\frac{1}{600}\right) = 10 \cdot \frac{\sqrt{3}}{2} \]

6. **Calculate the final value**:
\[ V\left(\frac{1}{600}\right) = 5\sqrt{3} \]

### Final Answer:
The instantaneous voltage at \( t = \frac{1}{600} \) seconds is \( 5\sqrt{3} \) volts.

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