you\'re working on a new high speed rail system. It uses 6000 horsepower electri

Question

you're working on a new high speed rail system. It uses 6000 horsepower electric locomotives that get their power from a single overhead trolley wire with a resistance of 15 m ohm/km. The electric current returns to the electrical substation through the railroad track that has negligible resistance. However, the voltage at the locomotive drops as the locomotive moves due to resistance in the overhead wire. Trolley Wire The locomotive design requires that the voltage at the locomotive must be at least 25,000 V. What is the current that the locomotive draws at 25,000 V and 6000 HP? 1 HP = 746 W How far from the power plant can the locomotive travel and not exceed a power loss m the wire of

Explanation / Answer

a) P = V*I

so I = P/V = 6000*746/ 25000 = 179.04A

b) power loss in the wire = 3% of total power used by the locomotive

so Ploss = 3/100* 6000*746 = 1.34E5 W

Ploss = I2R

R = R'*distance

so d = Ploss/I2*R' = 280km

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