A high voltage transmission line with a resistance of 0.31 O/km carries a curren

Question

A high voltage transmission line with a resistance of 0.31 O/km carries a current of 1000 A . THe line is at a potential of 700 kV at the power station and caries the current to a city located 160 km from the station. (a) What is the power loss due to resistance in the line? (b) What fraction of the transmitted power does this loss represent? A high voltage transmission line with a resistance of 0.31 O/km carries a current of 1000 A . THe line is at a potential of 700 kV at the power station and caries the current to a city located 160 km from the station. (a) What is the power loss due to resistance in the line? (b) What fraction of the transmitted power does this loss represent?

Explanation / Answer

Current I = 1000 A Potential difference ?V = 700 *10^3 V The transmission line with the resistance is 0.31 O / km Resistance R' = R d                         = 0.31 * 160 km                         = 49.6O a ) Power loss P_loss   = I^2 * R'                                  = ( 1000 )^2 * 49.6                                 = 49.6 MW                                 = 50 MW b ) Power input P _Input   = ? V * I                                         = 700 *10^3 V * 1000 A                                         = 700 MW    fraction of the power loss is P_loss / P _input                                              = 50 MW / 700 MW                                              = 7.14 %

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