A step-down transformer is used on a `1000 V` line to deliver `20A` at `120V` at the secondary coil. If the efficiency of the transformer is `80%` the current drawn from the line is.

Options

A. 3A
B. 30 A
C. 0.3A
D. 2.4 V

Explanation

To solve the problem, we need to find the current drawn from the line (I1) using the given information about the transformer and its efficiency.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Primary Voltage (V1) = 1000 V
- Secondary Voltage (V2) = 120 V
- Secondary Current (I2) = 20 A
- Efficiency (η) = 80% = 0.8

2. **Write the Efficiency Formula:**
The efficiency of a transformer is given by the formula:
\[ \eta = \frac{P_{out}}{P_{in}} \times 100 \]
Where:
- \( P_{out} \) = Output Power
- \( P_{in} \) = Input Power

3. **Calculate Output Power (P_out):**
The output power can be calculated using the formula:
\[ P_{out} = V2 \times I2 \]
Substituting the values:
\[ P_{out} = 120 \, \text{V} \times 20 \, \text{A} = 2400 \, \text{W} \]

4. **Calculate Input Power (P_in) Using Efficiency:**
Rearranging the efficiency formula to find \( P_{in} \):
\[ P_{in} = \frac{P_{out}}{\eta} \]
Substituting the values:
\[ P_{in} = \frac{2400 \, \text{W}}{0.8} = 3000 \, \text{W} \]

5. **Relate Input Power to Current:**
The input power can also be expressed as:
\[ P_{in} = V1 \times I1 \]
Substituting the known values:
\[ 3000 \, \text{W} = 1000 \, \text{V} \times I1 \]

6. **Solve for I1:**
Rearranging the equation to find \( I1 \):
\[ I1 = \frac{3000 \, \text{W}}{1000 \, \text{V}} = 3 \, \text{A} \]

### Final Answer:
The current drawn from the line is **3 A**.

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