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 they 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.

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?

/Worked Solutions/