Geometric circuit analysis

Abstract

The Smith rectangle symbolises the resistor and its width, height, aspect ratio, and area represent the current through, the voltage across, the resistance of, and the power dissipated in the resistor, respectively. In this article, the mosaic of rectangles (MOR) is introduced as a geometric approach to connected planar resistive network circuits with an ideal voltage source. In the MOR, the geometric Kirchhoff’s current and voltage laws are expressed as width and height conservations, respectively and are automatically satisfied. Four basic circuits are considered as applications of geometric circuit analysis. Resistors in series and in parallel are analysed using the MOR, and the effect of changing one resistor is visualised by superposing the initial and new MORs. The effect of loading an unloaded voltage divider with a parallel resistor is also visualised. The Wheatstone bridge is explored as an example of rather complicated resistive networks and the consistency of the assumed current directions, the shape of the MOR, and the geometric Kirchhoff’s laws is discussed. The geometric and game-like circuit analysis would be beneficial to high school and university students as well as their teachers.