To find the resistance of the secondary coil of an ideal transformer, we can follow these steps:
### Step 1: Understand the Power Relationship in an Ideal Transformer
In an ideal transformer, the power input to the primary coil is equal to the power output from the secondary coil. This can be expressed as:
\[
P_{input} = P_{output}
\]
Where:
- \( P_{input} = E_P \times I_P \) (Primary voltage times primary current)
- \( P_{output} = E_S \times I_S \) (Secondary voltage times secondary current)
### Step 2: Given Values
From the problem, we have:
- \( E_P = 1000 \, V \) (Primary voltage)
- \( I_P = 50 \, A \) (Primary current)
- \( E_S = 200 \, V \) (Secondary voltage for 80 houses)
### Step 3: Calculate the Input Power
Calculate the input power using the primary voltage and current:
\[
P_{input} = E_P \times I_P = 1000 \, V \times 50 \, A = 50000 \, W
\]
### Step 4: Calculate the Output Current
Using the power relationship, we can find the output current \( I_S \):
\[
P_{output} = P_{input} \implies E_S \times I_S = 50000 \, W
\]
Substituting \( E_S \):
\[
200 \, V \times I_S = 50000 \, W
\]
Solving for \( I_S \):
\[
I_S = \frac{50000 \, W}{200 \, V} = 250 \, A
\]
### Step 5: Calculate the Resistance of the Secondary Coil
The resistance of the secondary coil \( R_S \) can be calculated using Ohm's Law:
\[
R_S = \frac{E_S}{I_S}
\]
Substituting the values:
\[
R_S = \frac{200 \, V}{250 \, A} = 0.8 \, \Omega
\]
### Conclusion
The resistance of the secondary coil is approximately:
\[
R_S \approx 0.8 \, \Omega
\]
