A step down transformer converts line voltage from 1100 V to 220 V. The primary winding of transformer has 6000 turns and efficiency is 60% and output power is 9 kW. Find the input power:

Options

A. 10 kW
B. 15 kW
C. 20 kW
D. 25 kW

Explanation

To find the input power of the transformer, we can use the formula for efficiency. The efficiency (η) of a transformer is defined as the ratio of output power (P_out) to input power (P_in):

\[ \eta = \frac{P_{out}}{P_{in}} \]

Given:
- Output power (P_out) = 9 kW = \(9 \times 10^3\) W
- Efficiency (η) = 60% = 0.6

We can rearrange the formula to solve for input power (P_in):

\[ P_{in} = \frac{P_{out}}{\eta} \]

Now, substituting the known values into the equation:

\[ P_{in} = \frac{9 \times 10^3 \text{ W}}{0.6} \]

Calculating the input power:

\[ P_{in} = \frac{9 \times 10^3}{0.6} = 15 \times 10^3 \text{ W} = 15 \text{ kW} \]

Thus, the input power is 15 kW.

### Summary of Steps:
1. Write down the formula for efficiency: \(\eta = \frac{P_{out}}{P_{in}}\).
2. Rearrange the formula to find input power: \(P_{in} = \frac{P_{out}}{\eta}\).
3. Substitute the known values: \(P_{in} = \frac{9 \times 10^3 \text{ W}}{0.6}\).
4. Calculate the input power: \(P_{in} = 15 \text{ kW}\).