Electrical resistance between pairs of vertices of a conducting cube and continuum limit for a cubic resistor network

Malik Mamode (1)

1 PIMENT - Physique et Ingénierie Mathématique pour l'Énergie, l'environnemeNt et le bâtimenT

A method is given of determining analytically the driving-point resistance between any pair of vertices of: (i) a homogeneous conducting cube, (ii) a N X N X N cubic lattice of identical resistors. For the latter, the limit N‎ → ∞ is considered and the condition of the ohmic equivalence between these two systems is investigated.

Mots clés: driving-point resistance; finite cubic resistor network; Madelung constant; continuum limit

Domaines: Physique mathématique [math-ph]

Malik Mamode. Electrical resistance between pairs of vertices of a conducting cube and continuum limit for a cubic resistor network. Journal of Physics Communications, 2017, 1 (3), pp.035002. ⟨10.1088/2399-6528/aa8ab6⟩. ⟨hal-01619682⟩