The sinusoidal voltage wave changes from 0 to maximum value of 100 volt. The voltage when the phase angle is `30^(@)` will be –

Options

A. 70.7 Volt
B. 50 Volt
C. 109 volt
D. `-100` volt

Answer

To find the voltage when the phase angle is \(30^\circ\) for a sinusoidal voltage wave that changes from 0 to a maximum value of 100 volts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Maximum Voltage**:
The maximum voltage \( V_0 \) is given as 100 volts.

2. **Use the Sinusoidal Voltage Formula**:
The voltage \( V' \) at any phase angle \( \phi \) can be expressed using the formula:
\[ V' = V_0 \sin(\phi) \]

3. **Substitute the Phase Angle**:
Here, the phase angle \( \phi \) is \( 30^\circ \). We can substitute this value into the formula:
\[ V' = 100 \sin(30^\circ) \]

4. **Calculate \( \sin(30^\circ) \)**:
The value of \( \sin(30^\circ) \) is known to be \( \frac{1}{2} \).

5. **Substitute and Calculate the Voltage**:
Now substitute \( \sin(30^\circ) \) into the equation:
\[ V' = 100 \times \frac{1}{2} = 50 \text{ volts} \]

6. **Conclusion**:
Therefore, the voltage when the phase angle is \( 30^\circ \) is \( 50 \) volts.

### Final Answer:
The voltage when the phase angle is \( 30^\circ \) is **50 volts**.

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