The mass of one kilometer of an overhead wire on electrified railways is 890 kilograms. What is his resistance?

Given:

L = 1 kilometer = 1000 meters – the length of the contact wire;

m = 890 kilograms is the mass of a contact wire with a length L;

ro = 7800 kg / m3 – steel density;

k = 0.12 Ohm * mm2 / m – resistivity of steel.

It is required to determine the resistance of the contact wire R (Ohm).

Find the cross-sectional area of the contact wire:

S = V / L = (m / ro) / L = m / (ro * L) = 890 / (7800 * 1000) = 890/7800000 = 1.14 * 10-4 m2 = 114 mm2.

Then the resistance of the wire will be equal to:

R = k * L / S = 0.12 * 1000/114 = 120/114 = 1.05 Ohm.

Answer: the resistance of the contact wire is 1.05 ohm.