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, getting power from a single overhead wire with resistance 15 { m mOmega}/{ m km}, at 27 { m kV} potential relative to the track. Current returns through the track, whose resistance is negligible. Energy-efficiency standards call for no more than 3% power loss in the wire.

Part A

How far from the power plant can the train go and still meet this standard?

Express your answer using two significant figures.

Explanation / Answer

Given that,

Power P = 6000 HP = 4.47*10^6 W

resistance per unit length R / d = 15*10^(-6) ohm

V = 27*10^3 V

current i = P / V = 4.47*10^6 / 27*10^3

i = 165.55 A

Ploss = i^2*R = i^2*(R / d)*d

0.03*4.47*10^6 = (165.55)^2*15*10^(-6)*d

d = 326.2 km

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