  The order of the set of equivalent resistances, A(n) of n equal resistors
combined in series and in parallel has been traditionally addressed
computationally, for n up to 22. For larger n there have been constraints of
computer memory. Here, we present an analytical approach using the Farey
sequence 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 with
the strict upper bound, A(n) ~ 2.618^n, presented here. It is further shown
that the Farey sequence approach, developed for the A(n) is applicable to
configurations other than the series and/or parallel, namely the bridge
circuits and non-planar circuits. Expressions describing set theoretic
relations 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.
