The applied a.c power to a half-wave rectifier is 200W. The d.c power output obtained is 50W. The rectification efficiency is

Options

A. `12.5% `
B. `25%`
C. `37.5% `
D. ` 50% `

Answer

To find the rectification efficiency of a half-wave rectifier, we can follow these steps:

### Step 1: Understand the given values
- **AC Power Input (P_ac)** = 200 W
- **DC Power Output (P_dc)** = 50 W

### Step 2: Use the formula for rectification efficiency
The formula for rectification efficiency (η) is given by:

\[ \eta = \left( \frac{P_{dc}}{P_{ac}} \right) \times 100 \]

### Step 3: Substitute the known values into the formula
Now, substituting the values we have into the formula:

\[ \eta = \left( \frac{50 \, \text{W}}{200 \, \text{W}} \right) \times 100 \]

### Step 4: Calculate the efficiency
Calculating the fraction:

\[ \frac{50}{200} = 0.25 \]

Now, multiplying by 100 to convert it to a percentage:

\[ \eta = 0.25 \times 100 = 25\% \]

### Step 5: Conclusion
Thus, the rectification efficiency of the half-wave rectifier is **25%**.