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The conductor temperature varies linearly from an extremity to the other.Calculate the...

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lessoflot | Student, College Freshman | (Level 1) Honors

Posted June 30, 2009 at 12:49 AM via web

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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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neela | High School Teacher | (Level 3) Valedictorian

Posted June 30, 2009 at 1:01 PM (Answer #1)

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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.

 

 

 

 


 

 

 

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