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The order of the set of equivalent resistances, A(n) of n equal resistorscombined in series and in parallel has been traditionally addressedcomputationally, for n up to 22. For larger n there have been constraints ofcomputer memory. Here, we present an analytical approach using the Fareysequence with Fibonacci numbers as its argument. The approximate formula, A(n)~ 2.55^n, obtained from the computational data up to n = 22 is consistent withthe strict upper bound, A(n) ~ 2.618^n, presented here. It is further shownthat the Farey sequence approach, developed for the A(n) is applicable toconfigurations other than the series and/or parallel, namely the bridgecircuits and non-planar circuits. Expressions describing set theoreticrelations among the sets A(n) are presented in detail. For completeness,programs to generate the various integer sequences occurring in this study,using the symbolic computer language MATHEMATCA, are also presented.

The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel