A transformer is used to light a 140 W, 24 V lamp from 240 V AC mains. The current in mains cable is 0.7 A, find the efficiency of transformer.

Options

A. 0.48
B. 63.85
C. 0.833
D. 0.9

Answer

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

### Step 1: Calculate the Input Power
The input power (P_in) can be calculated using the formula:
\[ P_{\text{in}} = V_{\text{in}} \times I_{\text{in}} \]
where:
- \( V_{\text{in}} = 240 \, \text{V} \) (mains voltage)
- \( I_{\text{in}} = 0.7 \, \text{A} \) (current in mains cable)

Substituting the values:
\[ P_{\text{in}} = 240 \, \text{V} \times 0.7 \, \text{A} = 168 \, \text{W} \]

### Step 2: Identify the Output Power
The output power (P_out) is given as:
\[ P_{\text{out}} = 140 \, \text{W} \]

### Step 3: Calculate the Efficiency
Efficiency (\( \eta \)) of the transformer can be calculated using the formula:
\[ \eta = \left( \frac{P_{\text{out}}}{P_{\text{in}}} \right) \times 100\% \]

Substituting the values we calculated:
\[ \eta = \left( \frac{140 \, \text{W}}{168 \, \text{W}} \right) \times 100\% \]
\[ \eta = 0.8333 \times 100\% = 83.33\% \]

### Conclusion
The efficiency of the transformer is approximately:
\[ \eta \approx 83.33\% \]

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