Determine the mass of the copper wire for the 2 km line, if its resistance should be equal to 1.36 ohms.

Given:

l = 2 kilometers = 2000 meters – the length of the copper wire;

R = 1.36 Ohm – copper wire resistance;

r = 0.018 Ohm * mm2 / m – copper resistivity;

ro = 8900 kg / m3 – copper density.

It is required to determine m (kilogram) – the mass of the copper wire.

Find the cross-sectional area of the copper wire:

s = r * l / R = 0.018 * 2000 / 1.36 = 36 / 1.36 = 26.5 mm2 = 26.5 * 10-6 m2.

Let’s find the volume occupied by the copper wire:

V = s * l = 26.5 * 10-6 * 2000 = 53 * 10-3 m3.

Then the mass of the wire will be equal to:

m = ro * V = 8900 * 53 * 10-3 = 8.9 * 53 = 471.7 kilograms.

Answer: the mass of a copper wire is 471.7 kilograms.