I encountered a academic research problem to efficiently compute the current/voltage at each node of a rectangular resistor network. The rectangular resistor network that I have is defined by two things 1) the regular network topology, which you can consider it like meshgrids with one unit resistor on each edge; and 2) the knowledge of the state of each node (bad or good). For example, a 2x2 resistor network of my type (with all good node) is


simulate this circuit – Schematic created using CircuitLab

3x3 resistor networks of my type with all good nodes and one bad node(2,0) are given below.


simulate this circuit

In practice, a resistor network I might have to deal with is of size 300x500. I wonder whether there is some efficient method to compute the current/voltage at each node, when the good/bad nodes are known and the two nodes connected into the circuit is (0,0) and (299,499). I guess there should be some existing methods to this type of questions. Can anyone kindly help me?

  • \$\begingroup\$ Are all resistors the same value? \$\endgroup\$ – angelatlarge Mar 14 '13 at 19:18
  • \$\begingroup\$ Related: electronics.stackexchange.com/q/60458/17592 - with a general answer: electronics.stackexchange.com/a/60468/17592 \$\endgroup\$ – user17592 Mar 14 '13 at 19:19
  • \$\begingroup\$ Is a tool like Spice an option? \$\endgroup\$ – jippie Mar 14 '13 at 19:33
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    \$\begingroup\$ Current isn't measured at nodes. Voltage is measured at nodes, current is measured in loops. Net current at a node is zero and net voltage around a loop is zero. \$\endgroup\$ – Dave Tweed Mar 14 '13 at 20:09
  • \$\begingroup\$ Probably nobody is answering this because it is a classic Mesh/Nodal analysis but with a huge number of meshes making it tedious. Basically you wind up with a large system of equations, but there will be a pattern you can extract once you get started so you won't have to write out the whole 60,000 equations. Try researching Mesh Analysis, or Nodal Analysis. \$\endgroup\$ – Matt Mar 15 '13 at 1:27

In short you could do this by writing out the equations, but matrix algebra was invented so thousands of equations didn't need to be written out.

Here is a paper describing how this can be done assuming you know something about matrices. At this level its basically somewhere in between a circuit model and finite element method model.

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