What is the value of D.C. voltage in a half wave rectifier in converting AC. voltage V = 100 sin (314 t) into D.C.?

Options

A. 100 volt
B. 50 volt
C. 32 volt
D. 0

Explanation

To find the value of the DC voltage in a half-wave rectifier when converting the AC voltage \( V = 100 \sin(314t) \) into DC, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Peak Voltage (\( V_0 \))**:
The given AC voltage is in the form \( V = V_0 \sin(\omega t) \). Here, \( V_0 = 100 \) volts.

2. **Understand the Function of a Half-Wave Rectifier**:
A half-wave rectifier allows only the positive half of the AC waveform to pass through, effectively blocking the negative half. This means that the average (DC) voltage output can be calculated based on the peak voltage.

3. **Formula for DC Voltage in a Half-Wave Rectifier**:
The average DC voltage (\( V_{DC} \)) for a half-wave rectifier is given by the formula:
\[ V_{DC} = \frac{V_0}{\pi} \]
where \( V_0 \) is the peak voltage.

4. **Substitute the Peak Voltage into the Formula**:
Now, substituting \( V_0 = 100 \) volts into the formula:
\[ V_{DC} = \frac{100}{\pi} \]

5. **Calculate the Value**:
Using the value of \( \pi \approx 3.14 \):
\[ V_{DC} = \frac{100}{3.14} \approx 31.85 \text{ volts} \]

6. **Round Off the Answer**:
Rounding \( 31.85 \) volts gives us approximately \( 32 \) volts.

### Final Answer:
The value of the DC voltage in a half-wave rectifier converting the given AC voltage is approximately **32 volts**.

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