POLYGONS OF UNEQUAL RESISTORS

Consider an N-sided polygon made of resistors such that the resistance s connected vertices are 2G times those connected between the center a nd each vertex. Effective resistance between the center and a vertex o f such a polygon is obtained by a recursive procedure. The limiting va lue of the resistance for large N is found to be a fraction that is no t always irrational. The method developed is suitable even for cases w here 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.