Resistors in dual networks


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Date

2020

Publication Type

Journal Article

ETH Bibliography

yes

Citations

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Data

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.

Publication status

published

Editor

Book title

Volume

8 (2)

Pages / Article No.

255 - 263

Publisher

Institut Teknologi Nasional Bandung

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Dual graphs; Electrical networks; Equivalent resistance

Organisational unit

03874 - Hungerbühler, Norbert / Hungerbühler, Norbert check_circle

Notes

Funding

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