# Conductance and conductivity

What is the relationship between conductance and conductivity? Is there any formula that can explain their relationship?

Conductance is the extrinsic property while conductivity is the intrinsic property. This means that conductance is the property of an object dependent of its amount/mass or physical shape and size, while conductivity is the inherent property of the material that makes up the object. No matter how the object changes in terms of shape/size/mass, as long as it is made of the same material and the temperature remains the same, its conductivity does not change. Conversely, the conductance of a conductor changes with its cross-sectional area and length. Of course, a higher conductivity also gives an object a higher conductance. The formula that relates conductivity with conductance is:

$$G=\sigma \frac A l$$

where $G$ is the conductance, $σ$ the conductivity, $A$ the cross-sectional area perpendicular to the direction of electric current, and $l$ the length of the conductor. This formula applies for any (geometrically) prismic or cylindrical conductor, including cuboids.

• I guess the formula is for the 3D case. How about for a 2D, 1D, or even 0D system? Commented Feb 19, 2021 at 1:49
• @ΑλέξανδροςΖεγγ If your object is 2D or 1D (i.e. has zero thickness) there will be no actual material to conduct anything, so it would be 0. If you just have a very thin object with constant thickness then you can use formulas like $G = k\frac{\text{width}}{l}$ (where $k = \sigma \times \text{thickness}$) or $G = k \frac1{l}$ (where $k = \sigma A$), but really they are just the same formula with different arrangements of variables. At the end of the day you still have to either know the value of $A$ or experimentally measure the value of $k$. Commented Feb 19, 2021 at 2:57
• Then do the $k$s in the two cases have a proper name? Commented Feb 19, 2021 at 3:02
• @ΑλέξανδροςΖεγγ and if your object is 0D, it's essentially a point object. There isn't even a length to conduct across, and the formula boils down to something like $G = k$ where $k = \sigma \frac{A}{l}$, in which case we shouldn't bother about conductivity, since the whole formula literally say "conductance G equals constant k", which basically means that we're directly assigning a value to the conductance rather than calculating anything, and there may as well be no formula. Commented Feb 19, 2021 at 3:06
• @ΑλέξανδροςΖεγγ I've heard people call the resistivity versions "areal resistivity" and "linear resistivity", I suppose you can just replace "resistivity" with "conductivity", but it's not a very common term. If you preferred you could probably call it coefficient of conductance or something. Commented Feb 19, 2021 at 3:11