Circuit Analysis by Geometric Kirchhoff’s Laws

Abstract

An intuitive geometric method of circuit analysis is introduced through the example of the Wheatstone bridge. In this method, a resistor is expressed as a rectangle whose (horizontal) width and (vertical) height represent the current passing through and the potential difference across the resistor, respectively. Remarkably, Kirchhoff’s current and voltage laws for a connected planar resistive network with an ideal voltage source are simply expressed as the width and height conservation of the relevant rectangles in a mosaic of rectangles, respectively, where the laws are automatically satisfied, and sufficient to obtain a complete solution. These geometric Kirchhoff’s laws convert the solving of the resistive network into a mathematical game. Moreover, the geometric equivalence of the horizontal and vertical directions immediately generates the solution to the network dual to a connected planar resistive network. The geometric approach in this article shall intrigue university students and teachers alike in circuit analysis.