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The segment of circuit to be evaluated

I have already attempted this problem and it takes 6 wye-delta transformations to determine the equivalent resistance across the marked points. But I was looking for other possible methods that might simplify this approach. Note that I'm not asking for a solution. I'm asking for reasonable methods to apply to this context.

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  • \$\begingroup\$ Are you looking only for closed mathematical solutions? Or are you also wanting to see numerical approaches that might be used with code to also solve similar (and much more complex) problems? (I'm assuming you already know about nodal analysis and how to apply a linear matrix to this problem.) \$\endgroup\$
    – jonk
    Commented Jul 2, 2017 at 18:24
  • \$\begingroup\$ Well to be fair, the same approach can't possibly be used universally for all arrangements. So I'd like to know possibilities I may have missed in case of this particular circuit. A closed mathematical solution less time consuming than the one I mentioned in the description. \$\endgroup\$ Commented Jul 2, 2017 at 18:48
  • \$\begingroup\$ A general numerical procedure exists accepting any connected graph (with no cut-vertices.) I've used it for everything from estimating e-fields for complex objects to problems like this. Quite simple and quite general. The connected graph is trivial to represent in a matrix, as well. But I get your point about looking for only closed solutions. Now the only problem is deciding what is meant by "less time consuming." For me, that would be nodal analysis as the process of laying down the equations can be done in my sleep and I have free linear symbolic solvers. So that is what is "less" to me. \$\endgroup\$
    – jonk
    Commented Jul 2, 2017 at 19:38

2 Answers 2

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If you're happy to trade accuracy for speed, I'd note that the circuit is a 10 ohm in parallel with everything else. Everything else is going to work out to be at least 10 ohm, so Req is approximately 6 ohm. Good to within an order of magnitude.

For accuracy and generality it has to be nodal analysis (with a dummy source). Apply at every node and stick into a big matrix to be solved by a linear algebra package.

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One way is to apply Y-Δ transform in some places and calculate equivalent resistance for transformed circuit.

The othey way is to apply dummy voltage (i.e. 1V), solve circuit using either Kirschhoff laws or nodal analysis and calculate current flowing into the circuit from that source. By Ohms law you get equivalent resistance.

To double-check use software to simulate that circuit.

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