A copper wire with a cross-section of 0.03 mm squared and a length of 200 m is wound

A copper wire with a cross-section of 0.03 mm squared and a length of 200 m is wound on a coil. Find the resistance and mass of the wire.

Given:

s = 0.03 mm2 – cross-sectional area of ​​a copper wire wound on a coil;

l = 200 meters – the length of the copper wire;

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

ro = 8900 kg / m3 – copper density.

It is required to determine R (Ohm) – the resistance of the copper wire and m (kilogram) – its mass.

Let’s find the resistance of the wire:

R = r * l / s = 0.018 * 200 / 0.03 = 0.6 * 200 = 120 ohms.

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

V = s * l * 10-6 = 0.03 * 200 * 10-6 = 6 * 10-6 m3 (where 10-6 is the coefficient for converting square millimeters to square meters).

Then the mass of the wire will be equal to:

m = ro * V = 8900 * 6 * 10-6 = 8.9 * 6 * 10-3 = 53.4 * 10-3 kilograms = 53.4 grams.

Answer: the resistance of the wire is 120 ohms, its mass is 53.4 grams.