What is the mass of a copper wire with a length of 2 km and a resistance of 8.5 ohms?

Given:

R = 8.5 Ohm – copper wire resistance;

L = 2 kilometers = 2000 meters – copper wire length;

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

ro = 8900 kilograms per cubic meter.

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

Find the cross-sectional area of the wire:

S = k * L / R = 2000 * 0.018 / 8.5 = 4.2 mm2 = 4.2 * 10-6 m2.

Find the volume of copper wire:

V = S * L = 4.2 * 10-6 * 2000 = 8.4 * 10-3 m3.

Then the mass of the copper wire will be equal to:

m = ro * V = 8900 * 8.4 * 10-3 = 74.76 kilograms.

Answer: The mass of the copper wire is 74.76 kilograms.