Discussion Forum

If I understand you correctly, you have *attempted* to configure your two "parallel" halves to operate as classic resistors in parallel. Then, you concluded that the resistance in the middle would be 1/(1/2+1/4) = 4/3 ohm, which when added to the 1 ohm on each end (which are in series) would yield 3.3333 ohms.

But that analysis is NOT quite correct, BECAUSE:

(1) your computation of the analytic result assumed that the current paths in the center sections were independent, i.e., that there is zero current passing across the virtual surface between the two "separate" paths that now compose your middle block. That assumption is not justified, if all you did was put in a default (a continuity condition!) boundary to separate the two parts. So I suggest that you try enforcing an electrically-insulating boundary between the two halves and run it again. However, that change alone may still not be enough, because:

(2) Your resistors and connections do not have point like ends. Your analytic model assumed that the current distribution is completely uniform in each block and in only one direction. But you broke the symmetry of the problem when you made one path from a different conductivity material than the other. So the current distribution will flow in not-quite the directions you assumed! And that changed the resistance.

Thanks very much for time and detailed response. I definitely agree with you. While in each split domain, I originally felt that the field flow should run parallel to the virtual surface, so that current flow from one domain would be quite minimal. However, as you say, in order for current to enter the split domains, the current lines must deviate from their original parallel path and acquire a non-parallel component to accommodate the varying conductivities in the split domains. Do you know if people have incorporated "correction" factors into the simple analytical expression to correct for the geometric variations in this kind of situation? Or is it a matter of "it's easier to numerically work it out in COMSOL", i.e., integrate the current density on an electrode boundary? Thanks again!

I don't know if there exist any analytic expressions for the corrections you mention, although I suspect such techniques should be possible for relatively simple geometries (much like the many classic solutions to Laplace's equation). But in general, if I can't see an easy way to solve a problem analytically, and if it seems amenable to solution numerically, I go for the latter. Nowadays, the widespread availability of low-cost high-capability workstations, combined with software like Comsol Multiphysics, often makes that the best approach.