Almost all electrical conductors show a change in resistance with a change in temperature. An increase in temperature increases the amount of molecular agitation in a conductor, making it more difficult for charge to move through the same conductor. To an observer, the measured resistance of the conductor has increased with the change in temperature. This implies that meaningful resistance comparisons must be made for conductors of various sizes or materials at the same temperature.
Experimentation has shown that for every degree change in temperature above or below 20°C, the resistance of a pure conductor changes as a percentage of what it was at 20°C. This percentage change is a characteristic of the material and is known as the ‘temperature coefficient of resistance’. For copper at 20 degrees C, the coefficient is given as 0.00393; that is, each one degree change in temperature of a copper wire results in a change in resistance equal to 0.393 of one percent of its value at 20°C. For narrow temperature ranges, this relationship is approximately linear and can be expressed as:
R2 = R [1 + a(t2 – t1)]
Where:
R2 = resistance at temperature t2
R = resistance at 20 degrees C
t1 = 20 degrees C
a = temperature coefficient of resistance at 20 degrees C
For example:
Given the resistance of a piece of copper wire is 3.6 ohms at 20 degrees C. What is its resistance at t2 = 80 degrees C?
R2 = R [1 + a(t2 – t1)]
R2 = 3.60 [1 + 0.00393(80 – 20)]
R2 = 3.6 X 1.236 = 4.45 ohms
Using the above method, the heat rise (degrees C) in a transformer or relay winding can be accurately determined by measuring the winding resistance and performing the following calculation:
1) Measure the resistance of the cold winding (at room temperature approx. 20 degrees); call it R (ie 16 ohms).
2) Measure the ultimate resistance at the end of a heating run; call this R2 (ie 20 ohms)
3) Calculate the resistance ratio of the hot winding to that of the cold winding: R2 / R = 20 / 16 = 1.25
4) Subtract 1 from this ratio: 1.25 – 1 = 0.25
5) Divide this figure (0.25) by 0.00393: 0.25 / 0.00393 = 63.20 degrees C
In summary, we have shown that a change in temperature will affect the measured resistance of a pure conductor. We have also shown that this property can be exploited to calculate the heat rise in a winding from hot and cold resistance measurements.
