ON THE RESISTIVE FUNCTION MEASURED BETWEEN 2 POINTS ON A GRID OR A LATTICE OF SIMILAR NONLINEAR RESISTORS

The known problem of the resistance measured between two closest nodes on a grid of similar resistors, often considered in a linear version in physics and electrical engineering textbooks, is considered in a no n-linear version. An estimation, based on a simple polynomial model, s hows that with increase in the number of the dimensions of the grid (o r a lattice), the non-linearity of the characteristic of a single resi stor is expressed more and more weakly in the input resistive function , and that the input resistive function has the same (in the sense of the degrees involved and polarities of the coefficients) polynomial st ructure as the individual characteristic of the single resistor. (C) 1 998 John Wiley & Sons, Ltd.