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A town 20 km away from a power house receives 600 kW of power at 220 V. The power is transmitted via a line with resistance 0.4 ohm per km. The town gets power through a 3000 V to 220 V step-down transformer at a substation. Which of the following is/are correct?

1. The heat loss in the transmission line is 640 kW.
2. The heat loss in the transmission line is 1240 kW.
3. The plant must supply 1240 kW.
4. The plant must supply 640 kW.

Correct answer: The plant must supply 1240 kW.

Solution

The step-down transformer secondary is 220 V, primary is 3000 V. The town needs 600 kW at 220 V. Current in the transmission line (primary side of step-down = 3000 V): I = 600000 W / 3000 V = 200 A. Total line length = 2 * 20 km = 40 km. Total line resistance = 40 * 0.4 = 16 ohm. Power loss in line = I² * R = (200)² * 16 = 40000 * 16 = 640000 W = 640 kW. Total power plant must supply = 600 + 640 = 1240 kW.

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