Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Notes on "Temperature Coefficient of Resistivity"

The point of this experiment is to show you that the resistance of an object can change with temperature. That's not unusual -- most basic properties of materials change with temperature. But the real point is to show you how scientists can describe such a change mathematically ... and how they often choose to make linear approximations.

Suppose that some metal -- say, copper -- has a resistance which changes in a very simple manner as temperature changes:

                                                  
      resistance(T)  =  resistance(To)  +  A * (T - To)
                                                   

If this were true, then the coefficient A would give the absolute change in resistance for a given change in temperature:

                      resistance(T) - resistance(To)
             A    =   -------------------------------
	                          T  -  To

And, if you were to plot resistance versus temperature, the slope of the graph would always be A, no matter what temperature you choose as the reference To.

Question 1: What would the units of this coefficient be?

The graphs below show close-ups of the behavior of resistance as a function of temperature, near reference temperatures of To = 20 and To = 40 Celsius. Suppose that for copper, the value of A is exactly 1.0. Draw marks at the resistance values one degree above and below the reference temperature on each graph, and use them to draw a line on each graph showing resistance as a function of temperature.

Question 2: Are the slopes of the two graphs the same?

Now, if real copper behaved according to the above equation, with a coefficient of A = 1.0, then for any copper object, increasing the temperature by 1 degree Celsius would force the resistance to increase by 1 ohm. That would have to be true for all of these very different objects:

Question 3: Assuming the above relationship to be true, calculate the resistance of each of the 4 objects at T = 21 degrees.

Question 4: Does that make any sense?

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.