We know that resistance is dependent on both the materials resistivity and the geometry of the material. For a cylindrical or rectangular material the resistance is:
$$R=\rho*\frac{l}{A}$$
where l is the length and A the cross-sectional area.
In the same manner I understand that permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. When I look at capacitance I can see that it is dependent on the permittivity and the geometry. An example is the parallel plate capacitor's capacitance:
$$C=\epsilon\frac{A}{d}$$
where A is the area of the plates/dielectric and d the distance between the conductive plates.
Is capacitance the same as "permittance"? If not, what is the geometry dependent permittivity?
Best Answer
Look at the unit analysis: Resistivity is measured in Ω-m. When you mutliply by length (m) and divide by area (m2), you're left with just Ω.
Permittivity is measured in Farads/m. When you multiply by area (m2) and divide by spacing (m), you're left with just Farads, or capacitance.