The way I interpret the resistance \$R\$ of a resistor, which has dimensions \$ [\frac{\mathrm{V}}{\mathrm{A}}] \$ is: how many volts must be applied across the resistor to achieve 1 ampere of current?
The conductance \$G\$, which has dimensions \$ [\frac{\mathrm{A}}{\mathrm{V}}] \$ is then: how many amperes of current flow through the resistor when applying 1 volt?
I realize that these quantities are related to the geometry, whereas the resistivity \$ \rho = R\times \frac{A}{L} \$ which has dimensions \$ [\Omega \cdot \mathrm{m}] \$ is an intrinsic property of the material (doping of semi-conductor, electron/hole mobility, etc).
However, I cannot achieve an intuitive understanding to interpret the dimensions of resistivity. Can this be clarified?
Best Answer
\$\Omega\$m is the simplified unit of resistivity. The full unit is \$\Omega \$m\$^2/\$m. This means that a given length of material with a given cross sectional area will have a certain resistance whose value can be calculated using the resistivity.
For a 1 m length of material with a 1 mm\$^2\$ cross sectional area and a resistivity of 1:
\$1 \Omega \mathrm{m} = R(10^{-6}\mathrm{m}^2/1\mathrm{m})\$
\$R = {1\Omega \mathrm{m} \over(10^{-6}\mathrm{m}^2/1\mathrm{m})} = 10^6\Omega\$