In a step-down transformer the turn ratio is `1:2` and output power is `2.2kW`. If output current is `10A` then the values of input voltage and input current.

Options

A. `100 V, 20A`
B. `110V, 10A`
C. `440V,5A`
D. `440V, 20A`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- Turn ratio (Ns/Np) = 1/2
- Output power (P_out) = 2.2 kW = 2200 W
- Output current (I_out) = 10 A

### Step 2: Calculate the output voltage (V_out)
Using the formula for power:
\[ P_{\text{out}} = V_{\text{out}} \times I_{\text{out}} \]
Substituting the known values:
\[ 2200 = V_{\text{out}} \times 10 \]
To find \( V_{\text{out}} \):
\[ V_{\text{out}} = \frac{2200}{10} = 220 \text{ V} \]

### Step 3: Calculate the input voltage (V_in)
Using the turn ratio:
\[ \frac{N_s}{N_p} = \frac{V_{\text{out}}}{V_{\text{in}}} \]
Substituting the known values:
\[ \frac{1}{2} = \frac{220}{V_{\text{in}}} \]
Cross-multiplying gives:
\[ V_{\text{in}} = 220 \times 2 = 440 \text{ V} \]

### Step 4: Calculate the input current (I_in)
Using the turn ratio again:
\[ \frac{N_s}{N_p} = \frac{I_{\text{in}}}{I_{\text{out}}} \]
Substituting the known values:
\[ \frac{1}{2} = \frac{I_{\text{in}}}{10} \]
Cross-multiplying gives:
\[ I_{\text{in}} = \frac{10}{2} = 5 \text{ A} \]

### Final Values
- Input Voltage (V_in) = 440 V
- Input Current (I_in) = 5 A

### Summary of the Solution
The input voltage is 440 V and the input current is 5 A.

---