Electrical Resistivity and Conductivity - Resistance Versus Resistivity in Complicated Geometries

Resistance Versus Resistivity in Complicated Geometries

If the material's resistivity is known, calculating the resistance of something made from it may, in some cases, be much more complicated than the formula above. One example is Spreading Resistance Profiling, where the material is inhomogeneous (different resistivity in different places), and the exact paths of current flow are not obvious.

In cases like this, the formulas

need to be replaced with

where E and J are now vector fields. This equation, along with the continuity equation for J and the Poisson equation for E, form a set of partial differential equations. In special cases, an exact or approximate solution to these equations can be worked out by hand, but for very accurate answers in complex cases, computer methods like finite element analysis may be required.