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Electrical Properties of an Infinite Grid of Identical Resistors

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Naseem Rahman

Electrical properties of an infinite rectangular grid of identical resistors are investigated. A finite but unbounded model of such a grid is simulated on the computer and the results are compared to experimental data. The infinite grid is approached in the lab by constructing a toroidal grid, which though being finite, is unbounded and hence simulates the infinite situation well. The results of the computer simulation and the experiment are used for a theoretical understanding of the properties of the grid. The simulation was done on a Macintosh II computer using the WingZ spreadsheet. The powerful techniques of *Mathematica* for solving mathematical equations were utilized in trying to gain an understanding of the theory. The result found was that the equivalent resistance between two arbitrary points on an infinite rectangular grid of resistors was a function of [a modified] natural log of the distance between the two points...