The Sponge Resistor Model — A Hydrodynamic Analog to Illustrate Ohm's Law, the Resistor Equation R=ρℓ/A, and Resistors in Series and Parallel

Physics students encountering electric circuits for the first time often ask why adding more resistors to a circuit sometimes increases and sometimes decreases the resulting total resistance. It appears that these students have an inadequate understanding of current flow and resistance. Students who do not adopt a model of current, voltage, and resistance necessarily resort to memorizing formulas for calculating, e.g., the resistance of a resistor network. For these students, certain properties of electric circuits may remain mysterious or puzzling.