Temperature Dependence of Resistance
Electricity and Magnetism

Episode 110: Resistance and temperature

Lesson for 16-19 IOP TAP

This episode looks at the resistance of a metal and a semiconductor, giving a microscopic explanation of the variation with temperature. There is also a brief look at superconductivity and its applications.

Lesson Summary

  • Demonstration and discussion: Resistance and temperature (10 minutes)
  • Discussion: Free-electrons in metals (10 minutes)
  • Student experiment: Thermistor behaviour (20 minutes)
  • Discussion and demonstration: Conduction in semiconductors (5 minutes)
  • Discussion: Superconductivity (20 minutes)
  • Student activity: Researching superconductivity (30 minutes plus time for reporting back)
  • Student questions: Using these ideas (20 minutes)

Discussion and demonstrations: Resistance and temperature

This episode picks up on the variation of resistance of the filament lamp. Students’ own results should show that the resistance increases with current. Link this to the change of temperature of the wire and remind them that metals obey Ohm’s Law if the temperature is constant. (When they measured the resistance of the constantan wire in Episode 109, the current was always small, so temperature was almost constant.) You can reinforce the idea of resistance change in metals by cooling a wire and showing that its resistance decreases. This can be done using a cooling spray or, more dramatically, using liquid nitrogen (if this is available).

Episode 110-1: Metal resistance decreases as temperature falls (Word, 43 KB)

Discussion: Free-electrons in metals

It is worth pausing at this point to discuss the mechanism of metallic resistance. Remind students of the model whereby as temperature increases the thermal vibrations in the lattice increase causing more electron scattering. (Be aware that there is more here than meets the eye in terms of quantum, as opposed to classical, free electron theory). This increases the resistance of the metal.

Next consider semiconductors. Students are unlikely to know much about semiconductors so it may be worth giving a brief introduction by saying that, compared to metals, they have only a few free electrons, so resistance (resistivity is the more appropriate term here, but they have not yet met it) is much higher. However, semiconductors such as silicon are central to the electronics industry so it is well worth considering their electrical characteristics. For example, how does their resistance depend on temperature?

Student experiment: Thermistor behaviour

Students can investigate the temperature dependence of the resistance of a thermistor for themselves.

The results should show a clear decrease of resistance with increasing temperature. This is the opposite of what happened with the metal.

NB These thermistors are n.t.c. types (negative temperature coefficient). Other types exist which have a non-linear positive temperature coefficient.

Episode 110-2: Calibration of a thermistor (Word, 39 KB)

Discussion and demonstrations: Conduction in semiconductors

Ask whether the atoms in the semiconductor vibrate more at higher temperature. Of course they do – so this contribution to resistance must increase in the same way as for a metal. So what else could make the semiconductor conduct better? The answer is: more charge carriers. Whereas the number of free electrons in a metal is constant the effect of heating a semiconductor frees additional electrons (and holes, but it’s probably not worth mentioning them yet!). For silicon in this temperature range the effect of additional charge carriers outweighs the effect of additional vibrations.

An interesting additional demonstration can be done using a different semiconductor (carbon). This shows that the two effects compete with each other. At lower temperatures the increase in resistance due to vibration dominates, as temperature rises, more and more electrons are freed and the resistance begins to fall.

Discussion: Superconductivity

Having introduced the idea that metallic resistance is caused by electron scattering from ions as they vibrate you should return to what happens as a metal is cooled down.

You are looking for an argument that runs along the lines of: lower temperature, smaller amplitude of vibration so reduced scattering and therefore reduced resistance. Refer back to the initial demonstration.

How low can we go?

The students ought to predict that thermal vibrations will eventually stop (at absolute zero on a simple mechanical model). This implies a very low resistance at low temperatures (but not necessarily zero).

Lead into Kammerlingh Onnes’s work and his surprise that mercury’s resistance disappears at a very low temperature (a few degrees above absolute zero: 4.15 K).

This sudden transition was unexpected and is a quantum effect. It occurs for some but not all metals. It has also been observed at much higher temperatures (around 150 K) in certain ceramics. These are called high temperature superconductors (even though we are still talking about temperatures more than 100 degrees below zero Celsius! The mechanism for high temperature superconductivity is not fully understood and it is hoped that in future we may be able to manufacture room temperature superconductors.

Rather than lecture them about superconductors this would be a good opportunity to set them some research tasks which can be reported back to the class. Here is a work sheet that could be used:

Episode 110-3: Researching superconductivity (Word, 27 KB)

Student questions: Using these ideas

Episode 110-4: Filament lamp and thermistor in series (Word, 31 KB)

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