The applied a.c power to a full-wave rectifier is 400W. The d.c power output obtained is 200W. Rectifier efficiency is nearly

Options

A. 0.25
B. `37.5%`
C. 0.5
D. 0.75

Answer

To find the rectifier efficiency, we can follow these steps:

### Step 1: Understand the formula for rectifier efficiency
The efficiency (η) of a rectifier is calculated using the formula:
\[ \eta = \left( \frac{P_{dc}}{P_{ac}} \right) \times 100\% \]
where:
- \( P_{dc} \) is the output DC power,
- \( P_{ac} \) is the input AC power.

### Step 2: Identify the given values
From the problem statement, we have:
- \( P_{ac} = 400 \, \text{W} \)
- \( P_{dc} = 200 \, \text{W} \)

### Step 3: Substitute the values into the formula
Now, we can substitute the given values into the efficiency formula:
\[ \eta = \left( \frac{200 \, \text{W}}{400 \, \text{W}} \right) \times 100\% \]

### Step 4: Calculate the fraction
Calculating the fraction:
\[ \frac{200}{400} = 0.5 \]

### Step 5: Convert to percentage
Now, multiply by 100 to convert to percentage:
\[ \eta = 0.5 \times 100\% = 50\% \]

### Final Answer
The rectifier efficiency is nearly **50%**.

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