User:Inconspicuum/Physics (A Level)/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 ρ, 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.