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:

- a short copper wire of length 10 cm, with resistance R = 0.000 01 ohm at T = 20 degrees
- a long copper wire of length 10 m, with resistance R = 0.001 ohm at T = 20 degrees
- a translatantic copper cable, with resistance R = 100 ohm at T = 20 degrees
- a solid copper sphere, with resistance R = 0.000 000 001 ohm at T = 20 degrees

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?

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