Find the resistance at 50°c of copper wire 2mm in diameter and 3m long

0.0179 ohms for copper.

0.0184 ohms for annealed copper

Ď = R (A/l) where

Ď = electrical resistivity

R = electrical resistance of a uniform specimen

A = cross sectional area

l = length

Solve for R by multiplying both sides by l/A

R = Ď(l/A)

The cross section of the wire is pi * 1^2 mm = 3.14159 square mm = 3.14159e-6 square meters.

The length is 3 meters. So l/A = 3/3.14159e-6 = 9.5493e5

Ď for copper is 1.68e-8 so 1.68e-8 * 9.5493e5 = 1.60e-2 ohms at 20 C

But copper has a temperature coefficient (α) of 0.00386 per degree C.

So the resistance value needs to be adjusted based upon how far from 20 C the temperature is.

50 - 20 = 30 C

So 0.00386 * 30 = 0.1158 meaning that the actual resistance at 50 C will be 11.58% higher.

So 1.1158 * 0.016 = 0.0179 ohms.

If you're using annealed copper, the values for Ď and the temperature coefficient change.

Ď = 1.72e-8

α = 0.00393

Doing the math, you get

1.72e-8 * 9.5493e5 * (1 + 30 * 0.00393) = 0.0184 ohms