The conductor temperature varies linearly from an extremity to the other.Calculate the resistance of this conductor knowing it's resistance R1,2 at 2 extremes temperatures.
We record the conductor's resistance R1 and R2 at temperatures T1 and T2 .
We assume the conductor's resistance R0 at the T0 .
Call ,tr =Tr-T0, r=0,1,3.
By linearity of the resistance with temperature the resistance behaves as below:
R2=R0(1+a*t2) (2) where a is the temperature coefficient of resistance.
(1)/(2) eliminates R0:
R1/R2 = (1+a*t1)/(1+a*t2)
a(R1t2 -R2t1) = R2-R1
a is now kown.
Use this a to calculate the resistance R at a temperature T with a formula :
R = R0 [1+ a* (T-T0)] or
Hope this helps.