Episode 112: Resistivity
Lesson
for 16-19
- Activity time 110 minutes
- Level Advanced
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)