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. `30 %`
B. `50 %`
C. `90 %`
D. `10 %`

Explanation

To find the efficiency of the transformer, we need to calculate the input power and the output power and then use the formula for efficiency.

### Step-by-Step Solution:

1. **Identify the Output Power (P_out)**:
The output power is given as the power consumed by the lamp, which is:
\[ P_{\text{out}} = 100 \, \text{W} \]

2. **Calculate the Input Power (P_in)**:
The input power can be calculated using the formula:
\[ P_{\text{in}} = V_p \times I_p \]
where \( V_p \) is the primary voltage and \( I_p \) is the primary current. Given:
- \( V_p = 220 \, \text{V} \)
- \( I_p = 0.5 \, \text{A} \)

Substituting the values:
\[ P_{\text{in}} = 220 \, \text{V} \times 0.5 \, \text{A} = 110 \, \text{W} \]

3. **Calculate the Efficiency (η)**:
The efficiency of the transformer is given by the formula:
\[ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\% \]
Substituting the values we calculated:
\[ \eta = \frac{100 \, \text{W}}{110 \, \text{W}} \times 100\% \approx 90.91\% \]

4. **Round the Efficiency**:
For practical purposes, we can round this to approximately:
\[ \eta \approx 90\% \]

### Final Answer:
The efficiency of the transformer is approximately **90%**.