# Resistance versus Temperature

confused1
A copper wire has a resistance of 0.501 ohms at 20.0 degrees C, and an iron wire has a resistance of 0.487 ohms at the same temperature. At what temperature are their resistances equal?

Resistivity of Copper: .0039
Resistivity of Iron: .0005

Poncho
Try this formula

$$\frac{{\Delta R}}{R_0} = \alpha \Delta T$$

You need to look up the alpha

physbod
For pure metals the relationship is (almost) linear and the formula is:
R=R0[1+$$\alpha$$(T-T0)

FYI the figures quote are temperature coefficients measured in K-1 (degrees Celsius to the minus one is also fine, as the increments are the same. Just don't mix the two as values for T and T0 in one calculation):

Where you want the resistance to be equal, you just back the copper and iron halves of the equation together (copper on the left, iron on the right).

0.501 [1 + 0.0039 (T - 20)] = 0.487 [1 + 0.0005 (T - 20)]

Multiply the lot out, so as to separate T
0.501 + 0.0019539T - 0.039078 = 0.487 + 0.0002435T - 0.00487

Real numbers on the left, expressions in T on the right
0.501 - 0.487 - 0.039078 + 0.00487 = (0.0002435 - 0.0019539)T
-0.020208 = -0.0017104T

Divide both sides by -0.0017104
T=11.81478017 degrees Celsius

It you subs in [T-20] as -8.185 into either equation to double check, at T, the resistance will be about 0.485$$\Omega$$

6 years late, but hope this helps.

Last edited:
physbod
On reflection, I have noticed that Iron has a resistance temperature coefficient of 0.005K-1, not 0.0005K-1. The principle of working through it is still correct, but this answer is only correct for the question asked incorrectly ...if that makes any sense 