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How to Calculate Temperature Rise in Copper Windings from Resistance Measurements

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 by preventing the movement of charge through the same conductor. For 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 of temperature change above or below 20 degrees C, the resistance of a pure conductor changes as a percentage of what it was at 20 degrees C. This percentage change is a characteristic of the material and it is known as the “temperature coefficient of resistance.” For copper at 20 degrees C, the coefficient is given as 0.00393; that is, every one degree change in the temperature of a copper wire results in a resistance change equal to 0.393 of one percent of its value at 20 degrees C. For narrow temperature ranges, this relationship is approximately linear and can be expressed as:

R2 = R [1 + a(t2 – t1)]

Where:

R2 = resistance to temperature t2

R = resistance at 20 degrees C

t1 = 20 degrees C

a = temperature coefficient of resistance at 20 degrees C

For instance:

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 resistance of the winding and performing the following calculation:

1) Measure the resistance of the cold winding (at room temperature approx. 20 degrees); 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 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 used to calculate heat gain in a winding from heat and cold resistance measurements.

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