Proceedings - Mathematical Sciences

, Volume 122, Issue 2, pp 153-162

First online:

Farey sequences and resistor networks

  • SAMEEN AHMED KHANAffiliated withDepartment of Engineering, Salalah College of Technology Email author 

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In this article, we employ the Farey sequence and Fibonacci numbers to establish strict upper and lower bounds for the order of the set of equivalent resistances for a circuit constructed from n equal resistors combined in series and in parallel. The method is applicable for networks involving bridge and non-planar circuits.


Farey sequence Fibonacci numbers Lucas numbers resistor network bridge and non-planar circuits