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.



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Posted on (Answer #1)

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:

R1=R0(1+a*t1)           (1)

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)


R1*a*t2-R2*a*t1= R2-R1

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

R=R1[1+ a*(T-T1)]

Hope this helps.








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