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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.

1. 600 kW
2. 300 kW
3. 150 kW
4. 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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