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 wire line carrying power is 0.5 `Omega` per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station 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) Characterise the step up transformer at the plant.

Explanation

Line resistance `=30xx0.5=15Omega`.
rms current in the line `=(800xx1000W)/(4000V)=200A`
(a) Line power loss `=(200A)^(2)xx 15Omega=600kW.`
(b) Power supply by the plant `= 800 kW + 600 kW = 1400 kW.`
(c ) Voltage drop on the line `=200A xx 15Omega=3000V`.
The step-up transformer at the plant is `440V-7000V`.