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 less due to leakage? c. Characterise the step up transformer at the plant.

Explanation

Total line resistance ` = 0.5 xx 30 = 15`
a. Line power loss `=I_(rms)^2 R = (200)^2 xx 15 = 600 kW`
b. Power supplied = 800 + 600 = 1400 kW
c. Voltage dropped ` = I_(rms) R = 200 xx 15 = 3000 V`
Total voltage to be supplied = 4000 + 3000 = 7000 V
` therefore ` Step up transformer at the plant is 440 V/7000 V