Nearly all electrical conductors show a change in resistance with a change in temperature. A rise in temperature increases the amount of molecular agitation in a conductor hindering the movement of charge through the same conductor. To an observer, the measured resistance of the conductor has increased with the temperature change. This implies that meaningful comparisons of resistance for conductors of various sizes or materials must be performed at the same temperature.
Experimentation has shown that for each degree of temperature change above or below 20 degree C, the resistance of a pure conductor changes as a percent of what it was at 20 degree C. This percentage change is a characteristic of the material and is known as the ‘temperature coefficient of resistance’. For copper at 20 degree C the coefficient is given as 0.00393; that is, each change of one degree in the temperature of a copper wire results in a resistance change equal to 0.393 of one percent of its value at 20 deg 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 a 20 degree C
t1 = 20 degree C
a = temperature coefficient of resistance at 20 degree C
For example:
Given the resistance of a length 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 winding resistance cold (at room temperature approx. 20 deg); call it R (i.e. 16 ohms).
2) Measure the final resistance at the end of a heat run; call this R2 (i.e. 20 ohms)
3) Calculate the resistance ratio of the hot winding to that of the winding cold: 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.
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