A transformer is used to light a 200 W and 110 V lamp from a 220 V mains. If the main current is 1 amp, the efficiency of the transformer is approximately :

Options

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

Explanation

To solve the problem of finding the efficiency of the transformer, we can follow these steps:

### Step 1: Identify Given Values
- Power of the lamp (P_output) = 200 W
- Voltage of the lamp (V_output) = 110 V
- Voltage of the mains (V_input) = 220 V
- Current from the mains (I_input) = 1 A

### Step 2: Calculate Input Power (P_input)
The input power can be calculated using the formula:
\[ P_{input} = V_{input} \times I_{input} \]

Substituting the given values:
\[ P_{input} = 220 \, V \times 1 \, A = 220 \, W \]

### Step 3: Calculate Efficiency (η)
The efficiency of the transformer can be calculated using the formula:
\[ \eta = \left( \frac{P_{output}}{P_{input}} \right) \times 100 \]

Substituting the values we have:
\[ \eta = \left( \frac{200 \, W}{220 \, W} \right) \times 100 \]

### Step 4: Perform the Calculation
Calculating the fraction:
\[ \frac{200}{220} = 0.909 \]

Now, multiplying by 100 to get the percentage:
\[ \eta = 0.909 \times 100 = 90.9 \% \]

### Step 5: Approximate the Efficiency
Since the question asks for the approximate efficiency, we round 90.9% to the nearest whole number:
\[ \eta \approx 90\% \]

### Final Answer
Thus, the efficiency of the transformer is approximately **90%**.

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