Physics – General Physics
Scientific paper
2010-04-20
Physics
General Physics
37 Pages in MS Word, 6 Figures, 19 Integer Sequences, 3 Tables, and 9 Programs in MATHEMATICA. http://SameenAhmedKhan.webs.com
Scientific paper
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.
No associations
LandOfFree
The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-471886