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. `63.8%`
B. `74%`
C. `83.3%`
D. `48%`

Explanation

To find the efficiency of the transformer used to light a 140 W, 24 V lamp from a 240 V AC mains, we will follow these steps:

### Step 1: Identify the Input Power
The input power (Pi) can be calculated using the formula:
\[ P_i = V_p \times I_p \]
where:
- \( V_p = 240 \, V \) (input voltage)
- \( I_p = 0.7 \, A \) (input current)

Substituting the values:
\[ P_i = 240 \, V \times 0.7 \, A = 168 \, W \]

### Step 2: Identify the Output Power
The output power (P0) is given as the power consumed by the lamp, which is:
\[ P_0 = 140 \, W \]

### Step 3: Calculate the Efficiency
The efficiency (\(\eta\)) of the transformer can be calculated using the formula:
\[ \eta = \frac{P_0}{P_i} \times 100 \]

Substituting the values:
\[ \eta = \frac{140 \, W}{168 \, W} \times 100 \]

Calculating the efficiency:
\[ \eta = 0.8333 \times 100 = 83.33\% \]

### Final Answer
The efficiency of the transformer is approximately:
\[ \eta \approx 83.3\% \]

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