A step down transformer converts transmission line voltage from 11000 V to 220 V. The primary of the transformer has 6000 turns and efficiency of the transformer is 60%. If the output power is 9 kW, then the input power will be

Options

A. 11 kW
B. 12 kW
C. 14 kW
D. 15 kW

Explanation

To find the input power of the transformer, we can use the formula for efficiency. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Output power (\(P_s\)) = 9 kW = \(9 \times 10^3\) W
- Efficiency (\(\eta\)) = 60% = 0.6

2. **Recall the Efficiency Formula**:
- The efficiency of a transformer is given by the formula:
\[ \eta = \frac{P_s}{P_i} \]
where \(P_s\) is the output power and \(P_i\) is the input power.

3. **Rearrange the Efficiency Formula**:
- To find the input power (\(P_i\)), rearrange the formula:
\[ P_i = \frac{P_s}{\eta} \]

4. **Substitute the Known Values**:
- Substitute \(P_s\) and \(\eta\) into the equation:
\[ P_i = \frac{9 \times 10^3 \text{ W}}{0.6} \]

5. **Calculate the Input Power**:
- Perform the calculation:
\[ P_i = \frac{9000}{0.6} = 15000 \text{ W} \]
- Convert to kilowatts:
\[ P_i = 15 \text{ kW} \]

6. **Conclusion**:
- The input power of the transformer is \(15 \text{ kW}\).

### Final Answer:
The input power will be **15 kW**.