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. `96%`
B. `90%`
C. `99%`
D. `95%`

Explanation

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

### Step 1: Identify the given values
- Output Power (P_out) = 100 W
- Input Voltage (V_in) = 220 V
- Input Current (I_in) = 0.5 A

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

### Step 3: Calculate the Efficiency of the Transformer
The efficiency (η) of the transformer is given by the formula:
\[ \eta = \left( \frac{P_{out}}{P_{in}} \right) \times 100\% \]
Substituting the values we have:
\[ \eta = \left( \frac{100 \, \text{W}}{110 \, \text{W}} \right) \times 100\% \]

### Step 4: Perform the calculation
Calculating the fraction:
\[ \frac{100}{110} = 0.9091 \]
Now, multiplying by 100 to get the percentage:
\[ \eta = 0.9091 \times 100\% \approx 90.91\% \]

### Step 5: Round off the efficiency
Rounding off 90.91% gives us approximately 90%.

### Conclusion
The efficiency of the transformer is approximately **90%**.

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