Resistors in dual networks
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Author / Producer
Date
2020
Publication Type
Journal Article
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yes
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Abstract
Let G be a finite plane multigraph and G' its dual. Each edge e of G is interpreted as a resistor of resistance Re, and the dual edge e' is assigned the dual resistance Re':=1/Re. Then the equivalent resistance re over e and the equivalent resistance re' over e' satisfy re/Re+re'/Re'=1. We provide a graph theoretic proof of this relation by expressing the resistances in terms of sums of weights of spanning trees in G and G' respectively.
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published
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Journal / series
Volume
8 (2)
Pages / Article No.
255 - 263
Publisher
Institut Teknologi Nasional Bandung
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Edition / version
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Subject
Dual graphs; Electrical networks; Equivalent resistance
Organisational unit
03874 - Hungerbühler, Norbert / Hungerbühler, Norbert