A-level Physics (Advancing Physics)/Resistivity and Conductivity

Resistivity and conductivity are material properties: they apply to all examples of a certain material anywhere. They are not the same as resistance and conductance, which are properties of individual artefacts. This means that resistivity and conductivity only apply to a given object. They describe how well a material resists or conducts an electric current.

Symbols and Units
Resistivity is usually represented by the Greek letter rho (ρ), and is measured in Ω m. Conductivity is usually represented by the Greek letter sigma (σ), and is measured in S m−1.

Formulae
The formula relating resistivity (ρ) to resistance (R), cross-sectional area (A) and length (L) is:

$$\rho = \frac{RA}{L}$$

Conductivity is the reciprocal of resistivity, just as conductance (G) is the reciprocal of resistance. Hence:

$$\frac{1}{\sigma} = \frac{\frac{1}{G} \times A}{L} = \frac{1}{G} \times \frac{A}{L} = \frac{A}{GL}$$

$$\sigma = \frac{GL}{A}$$

You should be able to rearrange these two formulae to be able to work out resistance, conductance, cross-sectional area and length. For example, it all makes a lot more sense if we write the first formula in terms of &rho;, A and L:

$$R = \frac{\rho L}{A}$$

From this, we can see that the resistance of a lump of material is higher if it has a higher resistivity, or if it is longer. Also, if it has a larger cross-sectional area, its resistance is smaller.

Questions
1. A material has a conductivity of 106 S m−1. What is its resistivity?

2. A pure copper wire has a radius of 0.5mm, a resistance of 1 MΩ, and is 4680 km long. What is the resistivity of copper?

3. Gold has a conductivity of 45 MS m−1. What is the resistance of a 0.01m across gold connector, 0.05m long?

4. A strand of metal is stretched to twice its original length. What is its new resistance? State your assumptions.

5. Which has the greater resistivity: a plank or a piece of sawdust, made from the same wood? 6. What is the relation between time and resistance and length? /Worked Solutions/