Polygons of unequal resistors

Sidhu, Satinder S.

doi:doi:10.1119/1.17753

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American Journal of Physics -- September 1994 -- Volume 62, Issue 9, pp. 815

Polygons of unequal resistors

Satinder S. Sidhu

Department of Physics, Washington College, 300 Washington Avenue, Chestertown, Maryland 21620

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Consider an N‐sided polygon made of resistors such that the resistances connected between the vertices are 2G times those connected between the center and each vertex. Effective resistance between the center and a vertex of such a polygon is obtained by a recursive procedure. The limiting value of the resistance for large N is found to be a fraction that is not always irrational. The method developed is suitable even for cases where resistances making up the polygon are of arbitrary values so that conventional symmetry arguments would not be applicable. The results are applied to a uniform wire shaped into a circular wheel with evenly spaced spokes, and other wire frame structures.