Timeline for Matrix solution of an equivalent resistance circuit problem
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2011 at 2:43 | vote | accept | Hooked | ||
| Apr 9, 2011 at 7:35 | answer | added | Marek | timeline score: 8 | |
| Apr 9, 2011 at 5:35 | history | edited | Hooked | CC BY-SA 3.0 |
rephrased question
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| Apr 9, 2011 at 4:54 | comment | added | TROLLHUNTER | A more natural question is to first ask if there is known a general algorithm to find the equivalent reesistance for two points, given such a network. There is atleast an analogous thing for an arbitrary network of equal resistances mathworld.wolfram.com/ResistanceDistance.html | |
| Apr 9, 2011 at 4:40 | comment | added | Luboš Motl | I think it's misleading to use the word "matrix" for this table of numbers because there is no natural linear structure on this space, as far as I can see. So the formulae to invert the conductances to resistances won't be a natural linear algebra formula - it won't be a "function" of the matrix, in particular, it won't be the inverse matrix, I guess. The most striking deviation from the "matrix logic" is that the entries $C_{ii}$ are either zero or infinite. | |
| Apr 8, 2011 at 21:55 | comment | added | Marek | @David: you can use Fourier transform for that because there the graph is lattice and the resistance has translational symmetry. In general the underlying graph will have no such structure. It might not even make sense to talk about embedding into $k$-dim space (which we often take for granted). | |
| Apr 8, 2011 at 21:18 | comment | added | Qmechanic♦ | It should probably be pointed out that $C_{ij}$ is measured when all the other resistors are absent, while the sought-for equivalent resistance $R_{ij}$ is measure when all the resistors are present. Or do you have something else in mind? | |
| Apr 8, 2011 at 20:58 | comment | added | David Z | Neat question :-) I suspect that there may be something like this, since you can use the Fourier transform (essentially an infinite-dimensional linear transformation) to solve the problem in xkcd.com/356. | |
| Apr 8, 2011 at 20:45 | history | asked | Hooked | CC BY-SA 3.0 |