insu-03590020
https://insu.hal.science/insu-03590020
doi:10.1088/1361-6404/ac0b4e
[INSU] INSU - Institut National des Sciences de l'Univers
[AFRIQ] HAL-Francophonie, Afrique et océan indien
[CNRS] CNRS - Centre national de la recherche scientifique
[IPGP] Institut de Physique du Globe de Paris
[UNIV-PARIS] Université Paris Cité
[UNIVERSITE-PARIS] Université Paris Cité
[ANR] ANR
Symmetries, recurrence, and explicit expressions of two-point resistances in 2 × n globe resistor networks
Perrier, Frédéric
Girault, Frédéric
[SDU] Sciences of the Universe [physics]
ART
two-point resistance
resistor networks
Kennelly's theorem
van Steenwijk's method
axial symmetry
Resistor networks are practical electric circuits and provide meaningful models to represent natural or artificial conductive structures. They can also be used to demonstrate how, in physics, general properties can be derived elegantly by combining general principles with symmetry properties. Here, this typical approach of physics is illustrated in the case of two-point resistances in the 2 × n globe network. It is a particular case of resistor networks on a sphere, where the n nodes of an equatorial frame of n identical resistors are connected by equal resistors to two axial poles. Recurrence relations are obtained using only Kirchhoff's laws and Kennelly's theorem. When complementing with relations derived using van Steenwijk's method, explicit relations are obtained for all two-point resistances to any order n. Such analytical exact results are useful to test the results of numerical or integral methods. This complete treatment of the 2 × n globe network can be used to illustrate for students the efficient ways of physics to derive analytical results and understand their origin.
2021
en
European Journal of Physics