• Support PF! Buy your school textbooks, materials and every day products Here!

Resistance versus Temperature

  • Thread starter confused1
  • Start date
  • #1
21
0
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
 

Answers and Replies

  • #2
29
0
Try this formula

[tex]\frac{{\Delta R}}{R_0} = \alpha \Delta T[/tex]


You need to look up the alpha
 
  • #3
2
0
For pure metals the relationship is (almost) linear and the formula is:
R=R0[1+[tex]\alpha[/tex](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[tex]\Omega[/tex]

6 years late, but hope this helps.
 
Last edited:
  • #4
2
0
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 :smile:
 

Related Threads for: Resistance versus Temperature

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
0
Views
3K
  • Last Post
Replies
1
Views
302
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
10K
  • Last Post
Replies
7
Views
6K
  • Last Post
Replies
24
Views
2K
Top