A high-voltage transmission line with a resistance of 0.31 Ohm/km carries a curr

Question

A high-voltage transmission line with a resistance of 0.31 Ohm/km carries a current of 1050 A. The line is at a potential of 650 kv at the power station and carries the current to a city located 162 km from the station. What is the power loss due to resistance in the line? What fraction of the transmitted power does this loss represent? The power supplied to a typical black-and-white television set is 86 W when the set is connected to 120 V. How much electrical energy does this set consume in 1 hour? A color television set draws about 2.4 A when connected to 120 V. How much time is required for it to consume the same consumes in 1 hour?

Explanation / Answer

4) Resistance = 162 km x 0.31 = 50.22 ohms
power loss = i^2 R = 1050^2 x 50.22 = 55.4 MW this is very high

Power of line = IV = 1050 x 650000 = 682.5 MW

So the power loss represents 8.12 percent

5) a) Energy = Power * Time
where energy is in joules, power in watts and time in seconds.

E = 86 W * 3600 s = 309600 J = 309.6 kJ

b) Power used by color set = 120 V * 2.4 A = 288 W

Time = Energy / Power = 309600/288
Time = 1075 s = 17.92 minutes

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