Your working on a new high speed rail system. It uses 6000 horsepower electric l
ID: 1438982 • Letter: Y
Question
Your 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 mOhm/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. a) 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 b) How far from the power plant can the locomotive travel and not exceed a power loss in the wire of greater than 3% of the power used by the locomotive?Explanation / Answer
a) let I be the current
the power each locomotive draws is product of voltage and current
power=V*I
hence I = P/V = 6000*746/25000 = 179.04 ampers
b) power loss = 3*power/100 = 3*6000*746/100 = 134280 watts
power loss = V2/R
let length upto which it can drive be x meters hence total resistance of wire will be 15*10-3*x
hence we have
134280=25000^2/ 15*10-3*x
we get x =310296.89km
c)
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