# 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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### 1 Answer

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(1+at2)=R2(1+at1)

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

a(R1t2 -R2t1) = R2-R1

**a=(R2-R1)/(R1t2-R2t1).**

**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.