To solve the problem step by step, we will use the principles of transformers and the relationships between voltage, current, and turns in the coils.
### Step 1: Write down the given data
- Number of turns in the primary coil, \( N_p = 300 \)
- Number of turns in the secondary coil, \( N_s = 150 \)
- Output power, \( P_{out} = 2.2 \, \text{kW} = 2200 \, \text{W} \)
- Current in the secondary coil, \( I_s = 10 \, \text{A} \)
### Step 2: Use the turns ratio to find the relationship between primary and secondary voltages
The relationship between the number of turns and the voltages in a transformer is given by:
\[
\frac{N_p}{N_s} = \frac{V_p}{V_s}
\]
Substituting the known values:
\[
\frac{300}{150} = \frac{V_p}{V_s}
\]
This simplifies to:
\[
2 = \frac{V_p}{V_s}
\]
Thus, we can express the primary voltage in terms of the secondary voltage:
\[
V_p = 2V_s
\]
### Step 3: Calculate the secondary voltage using the output power
The output power of the transformer can also be expressed as:
\[
P_{out} = V_s \cdot I_s
\]
Substituting the known values:
\[
2200 = V_s \cdot 10
\]
From this, we can solve for \( V_s \):
\[
V_s = \frac{2200}{10} = 220 \, \text{V}
\]
### Step 4: Find the primary voltage using the relationship derived from the turns ratio
Now that we have \( V_s \), we can find \( V_p \):
\[
V_p = 2V_s = 2 \times 220 = 440 \, \text{V}
\]
### Step 5: Calculate the input current using the power relationship
For an ideal transformer, the input power equals the output power:
\[
P_{in} = P_{out}
\]
This can be expressed as:
\[
V_p \cdot I_p = V_s \cdot I_s
\]
Substituting the known values:
\[
440 \cdot I_p = 220 \cdot 10
\]
This simplifies to:
\[
440 \cdot I_p = 2200
\]
Now, we can solve for \( I_p \):
\[
I_p = \frac{2200}{440} = 5 \, \text{A}
\]
### Final Results
- Input Voltage \( V_p = 440 \, \text{V} \)
- Input Current \( I_p = 5 \, \text{A} \)
### Summary
The input voltage and current in the primary coil are:
- \( V_p = 440 \, \text{V} \)
- \( I_p = 5 \, \text{A} \)
