Kirchhoff and Ohm in action: solving electric currents in continuous extended media

Abstract

In this paper we show a simple and versatile computational simulation method for determining electric currents and electric potential in 2D and 3D media with arbitrary distribution of resistivity. One of the highlights of the proposed method is that the simulation space containing the distribution of resistivity and the points of external applied voltage are introduced by means of digital images or bitmaps, which easily allows simulating any phenomena involving distributions of resistivity. The simulation is based on the Kirchhoff's laws of electric currents and it is solved by means of an iterative procedure. The method is also generalised to account for media with distributions of reactive impedance. At the end of this work, we show an example of application of the simulation, consisting in reproducing the response obtained with the geophysical method of electric resistivity tomography in presence of soil cracks. This paper is aimed at undergraduate or graduated students interested in computational physics and electricity and also researchers involved in the area of continuous electric media, which could find a simple and powerful tool for investigation.