It is straightforward to construct the set of equivalent resistance for circuits constructed from a bunch of four or five equal resistors. But as the bunch size increases it becomes difficult to find the order of the set of equivalent resistances. Even the computer programs runs out of memory. Here we present an analytical result using simple mathematical machinery. The size of the set is shown to be less than 2.618n.
KeywordsResistors series parallel bridge non-planar Fibonacci numbers Haros-Farey sequence integer sequences
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- Alvin Halpern, 3000 Solved Problems in Physics, Schaum’s Solved Problem Series, McGraw-Hill, 1988; Sameen Ahmed Khan, Lecture Notes in Physics, Salalah College of Technology E-Learning Website, http://www.sct.edu.om/ 2010.
- Robert L Boylestad, Introductory Circuit Analysis, 11th Edition, Pearson International, Prentice Hall, 2007. http://www.prenhall.com/boylestad/
- Neil J A Sloane (Ed.), The On-Line Encyclopedia of Integer Sequences 2008, published electronically at http://www.research.att.com/~njas/, http://oeis.org/; The OEIS Foundation Inc. http://www.oeis.org/ 2010. For many of the sequences, OEIS also has the computer programs, which may be run on faster computers to generate additional terms. The sequences cited in this article are: Sequence A000045, Sequence A000084, Sequence A005728, Sequence A048211, Sequence A153588, and Sequence A176502. Additional sequences at http://oeis.org/wiki/User:Sameen_Ahmed_Khan
- Eric W Weisstein, MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/
- Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, 37 pages, E-Print archive: http://arxiv.org/abs/1004.3346/ (21 April 2010).