A transformer is used to light a 60 W and 110 V lamp from 220 V mains. If the main current is 1.5 A, what is the efficiency of the transformer?

Options

A. 0.1818
B. 0.3191
C. 0.7523
D. 0.8327

Explanation

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

### Step 1: Identify the given values
- Output power (PS) = 60 W
- Output voltage (VS) = 110 V
- Input voltage (VP) = 220 V
- Input current (IP) = 1.5 A

### Step 2: Calculate the input power (PP)
The input power (PP) can be calculated using the formula:
\[ PP = VP \times IP \]
Substituting the known values:
\[ PP = 220 \, \text{V} \times 1.5 \, \text{A} \]
\[ PP = 330 \, \text{W} \]

### Step 3: Calculate the efficiency of the transformer
The efficiency (η) of the transformer is given by the formula:
\[ \eta = \frac{PS}{PP} \times 100\% \]
Substituting the values we have:
\[ \eta = \frac{60 \, \text{W}}{330 \, \text{W}} \times 100\% \]
\[ \eta = 0.1818 \times 100\% \]
\[ \eta = 18.18\% \]

### Final Answer
The efficiency of the transformer is approximately **18.18%**.

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