Determine the resistance and length of a copper wire weighing 89 g and a cross section of 0.1 mm ^ 2

Given:

m = 89 grams = 0.089 kilograms – the mass of the copper wire;

s = 0.1mm2 – cross section of copper wire;

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

ro = 8900 kg / m3 – copper density.

It is required to determine l (meter) – the length of the copper wire and its total resistance R (Ohm).

Let’s find the volume occupied by the wire:

V = m / ro = 0.089 / 8900 = 0.00001m3 = 10000mm3.

Then the length of the wire will be:

l = V / s = 10000 / 0.1 = 100000 millimeters = 100 meters.

The total resistance of the wire will be equal to:

R = r * l / s = 0.018 * 100 / 0.1 = 1.8 / 0.1 = 18 ohms.

Answer: the length of the copper wire will be 100 meters, its total resistance is 18 ohms.