Resistance temperature equation 2

[Electrical1948]

Hi all,

In the IEC standards for transformer and motors the following formula is provided for calculating the resistance at temperature Θ2:

R2/R1 = (Θ2 + 235) / (Θ1 + 235)

235 = copper

In University I learned the following equation: R2/R1 = (1 + 𝛼(Θ2-Θ1)

What is the difference?

 

[electricpete]

In real life there is a measured curve which may not easily be fit by a single simple equation across a wide range

R2/R1 = (1 + 𝛼(Θ2-Θ1)) is a simple equation which captures the slope of the curve at a given point. (I think 20C is common).

R2/R1 = (Θ2 + 235) / (Θ1 + 235) is non-linear. I think it is created to fit the general behavior of the curve over the range where we might often be correcting winding resistance (let's say 10C - 100C). We can tell it doesn't apply across a wide temperature range because it would predict zero resistance at T=-235C (which is still above absolute zero -273C).

I suggest try using Θ1=20C and Θ2 =40C and select alpha corresponding to copper and plug it in to both equations to see how close they come to giving the same ratio of resistances. I'll wager that it comes close (but not exact).

 

[Gr8blu]

Just for clarity - the constant in that IEC equation has been approximated. The actual value is 234.5 not "235".
Also note that temperature(s) need to be in degrees Celsius.

As noted by electricpete - the OP's "university" equation is looking at the slope of the curve at a single point. Different metals are taken at different base points, but for typical conductors (copper, gold, aluminum, platinum) the "slope point" where the equation is most accurate is 20 C.

Converting energy to motion for more than half a century

 

[che12345]

Mr. Electrical1948 (Electrical)(OP)13 Jul 23 18:24
"....In the IEC standards for transformer and motors the following formula is provided for calculating the resistance at temperature Θ2: R2/R1 = (Θ2 + 235) / (Θ1 + 235), 235 = copper. In University I learned the following equation: R2/R1 = (1 + 𝛼(Θ2-Θ1). What is the difference?"
I try to answer as following for your consideration.
1. Basic R= (l x p)/A.
2. At 20deg C:
a) for copper, soft p=0.01754 (mm2 ohm/m) , a=4.0 x 10 [sup]-3[/sup](K[sup]-1[/sup]).
b) for copper, hard p=0.01786 (mm2 ohm/m) , a=3.92 x 10 [sup]-3[/sup](K[sup]-1[/sup]).
3. For temperature from -50 to +200deg C:
p2 = p20 [1+a(t2-20)]. therefore R2=(l/A) p20[1+a(t2-20).
3.1. Resistance R2/R1=[1+ a(t2-t1)].
4. Simplified formula
R2/R1 = (Θ2 + 235) / (Θ1 + 235), 235 = copper.
Che Kuan Yau (Singapore)

 

[Electrical1948]

Hi

I found the answer. The material temperature correction factor is the same as the temperature coefficient as follows:

𝛼 = 1/(235+20) = 0.003937