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A town needing 800 kW at 220 V lies 15 km from a power plant that generates at 440 V. The two-wire transmission line has resistance 0.5 ohm per km (each wire), and the town steps the supply down with a 4000-220 V transformer at a substation. The plant uses a step-up transformer feeding the line at 4000 V. Estimate the power lost as heat in the transmission line.
- 600 kW
- 300 kW
- 150 kW
- 1200 kW
Correct answer: 600 kW
Solution
The line carries the town's power at 4000 V, so I = 800000/4000 = 200 A. Total resistance of the two 15-km wires = 0.5*15*2 = 15 ohm. Line power loss = I² R = 200² * 15 = 40000*15 = 600000 W = 600 kW.
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