Resistivity
Electricity and Magnetism

Episode 112: Resistivity

Lesson for 16-19 IOP TAP

In this episode, students learn how and why the resistance of a wire depends on the wire’s dimensions. They learn the definition of resistivity and use it in calculations.

Lesson Summary

  • Discussion: Variation of resistance with length and area (5 minutes)
  • Student experiment: Variation of resistance with length and area (30 minutes)
  • Discussion: Variation of resistance with length and area (10 minutes)
  • Student experiment: Measurement of resistivity (30 minutes)
  • Student questions: Using these ideas (30 minutes)

Discussion: Variation of resistance with length and area

The analogy to water flow will be useful here – ask them how they think the flow rate will be affected if you increase the cross-sectional area or length of the pipe along which the water has to flow. This should lead to two predictions about the resistance of a wire:

  • resistance increases with length
  • resistance decreases with diameter or cross-sectional area

It will be worth reminding them that doubling the diameter quadruples the cross-sectional area; many students get confused about the distinction and expect a wire of double diameter to have half the resistance.

Student experiment: Variation of resistance with length and area

You could ask them to do one or both of the following experiments. Both reinforce the idea that resistance depends on material dimensions:

Episode 112-1: How the dimensions of a conductor affect its resistance (Word, 44 KB)

Episode 112-2: Introduction to resistivity using conducting paper (Word, 49 KB)

Discussion: Variation of resistance with length and area

Follow up with some theory suggesting:

Resistance is proportional to length l

Resistance is inversely proportional to cross-sectional area A

resistance = constant  ×  lengthcross-section area

The constant is a property of the material used – its resistivity ρ.

R = ρ  ×  lA

The units of resistivity can be derived from the equation:  Ω m.

Emphasise that this is ohm metre, not ohm per metre.

Discuss the great range of resistivities amongst materials. Values for metals are very small. The resistivity of a material is numerically equal to the resistance between opposite faces of a one-metre-cube of the material; although this is not a good definition of resistivity, imagining such a block of metal does indicate why its value should be so low (~ 10-9 Ω m).

Student experiment: Measurement of resistivity

Complete this section by asking your students to measure the resistivity of several metal wires.

This experiment provides an opportunity for a detailed discussion of the treatment of experimental errors.

Episode 112-3: Measuring electrical resistivity (Word, 30 KB)

Student questions: Using these ideas

Problems involving resistivity.

Students often get confused between cross-section area and diameter.

Make sure they are able to convert mm2 to m2 for resistivity calculations.

Episode 112-4: Electrical properties (Word, 28 KB)

Download this episode

Resistivity
appears in the relation R=ρL/A σ=1/ρ
Limit Less Campaign

Support our manifesto for change

The IOP wants to support young people to fulfil their potential by doing physics. Please sign the manifesto today so that we can show our politicians there is widespread support for improving equity and inclusion across the education sector.

Sign today