A transformer is used to light a `100 W` and `110 V` lamp from a `220V` mains. If the main current is `0.5 A`, the Efficiency of the transformer is approximately:

Options

A. (a)0.3
B. (b)0.5
C. (c)0.9
D. (d)0.1

Explanation

To find the efficiency of the transformer, we can follow these steps:

### Step 1: Identify the given values
- Power of the lamp (Output Power, \( P_{out} \)) = 100 W
- Voltage of the lamp (Output Voltage, \( V_{out} \)) = 110 V
- Mains Voltage (Input Voltage, \( V_{in} \)) = 220 V
- Mains Current (Input Current, \( I_{in} \)) = 0.5 A

### Step 2: Calculate the Input Power
The input power (\( P_{in} \)) can be calculated using the formula:
\[ P_{in} = V_{in} \times I_{in} \]
Substituting the values:
\[ P_{in} = 220 \, \text{V} \times 0.5 \, \text{A} = 110 \, \text{W} \]

### Step 3: Calculate the Efficiency of the Transformer
The efficiency (\( \eta \)) of the transformer can be calculated using the formula:
\[ \eta = \left( \frac{P_{out}}{P_{in}} \right) \times 100 \]
Substituting the values:
\[ \eta = \left( \frac{100 \, \text{W}}{110 \, \text{W}} \right) \times 100 \]
\[ \eta = \left( 0.909 \right) \times 100 \approx 90.9\% \]

### Step 4: Conclusion
The efficiency of the transformer is approximately \( 90.9\% \).