A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two line wires carrying power is `0.5 Omega` per km. The town gets power from the lines through a 4000-220 V step down transformer at a substation in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply. assuming there is negligible power loss due to leakage?
(c) Characterize the step up transformer at the plant.

Explanation

Let's solve the problem step by step:

### Given Data:
- Power demand of the town, \( P = 800 \, \text{kW} = 800 \times 10^3 \, \text{W} \)
- Voltage at the plant, \( V_1 = 4000 \, \text{V} \)
- Distance from the plant to the town, \( d = 15 \, \text{km} \)
- Resistance of the line per km, \( R_{\text{line}} = 0.5 \, \Omega/\text{km} \)
- Total resistance of the line, \( R = 2 \times R_{\text{line}} \times d = 2 \times 0.5 \, \Omega/\text{km} \times 15 \, \text{km} \)
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