Temperature dependence of Resistance

[zorro]

Homework Statement

A wire has a resistance of 2 ohm at 25 C and 2.5 ohm at 100 C . Find the temperature coefficient of resistance of the wire.

The Attempt at a Solution

This question is a very easy one, but I had a doubt -
R=R_o(1 + αθ)
Here θ is the change in temperature.

I proceed in 2 ways:
1) We can take R_o = 2 ohm at 25 C so that the equation becomes
2.5 = 2 [1 + α(100-25)]
On solving, α=3.33 x 10^-3

2) Take R_o as the resistance at 0 C

2 = R_o(1 + 25α)
2.5 = R_o(1 + 100α)

On solving, α = 3.64 x 10^-3

Which one is correct and why?

 

[rock.freak667]

How do you know the resistance at 0C?

 

[rl.bhat]

R1 = Ro( 1 + αθ1)

R2 = Ro(1 + αθ2)

When you solve for α, you will get

α = (R2 - R1)/(R1θ2 - R2θ1)

Now find α.

 

[zorro]

How do you know the resistance at 0C?

I don't know the resistance. On dividing the two equations, R_o gets cancelled.

 

[zorro]

R1 = Ro( 1 + αθ1)

R2 = Ro(1 + αθ2)

When you solve for α, you will get

α = (R2 - R1)/(R1θ2 - R2θ1)

Now find α.

Why can't we use just one equation as I showed?...thats my doubt.

 

[rl.bhat]

In the first case, we get mean temperature coefficient of resistance for a selected pair of temperatures.

In the second case, it is the actual α for particular temperature.

 

[zorro]

In the first case, we get mean temperature coefficient of resistance for a selected pair of temperatures.

In the second case, it is the actual α for particular temperature.

Is it that the actual temperature coefficient of resistance is measured w.r.t. the resistance at 0 C?

 

[rl.bhat]

Is it that the actual temperature coefficient of resistance is measured w.r.t. the resistance at 0 C?

Yes. In the table of constants, α for different materials is given for 20^oC.