## 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 × *l**A*

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 mm^{2} to m^{2} for resistivity calculations.

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