Theoretical Study on Geometries of Electrodes in Laboratory Electrical Resistivity Measurement

Abstract

Electrical resistivity tests have been widely conducted in multiple scales, from a few centimeters to kilometers. While electrode spacing is used to define field resistance, laboratory measurements in a limited space need to consider electrode geometry. However, there are no studies that theoretically explore the effects of the geometries of electrodes and container size on laboratory electrical resistivity measurements. This study formulates a theoretical electrical resistance for the geometry of cylindrical electrodes and the size of a non-conductive container with the method of image charges. As a complementary study, experimental tests were conducted to verify the derived equations. The discussion includes the concepts of the spherical equivalent electrodes and a simple design method for container size.