A tool for predicting the current distribution in systems where heat is generated through resistance heating of molten materials such as slags is crucial for understanding and controlling many industrial processes. There is very little information available in published literature to provide a comprehensive understanding of the complex relation between the properties of the slag, the geometry of the system, the heat generated and the heat lost The 'shell model' is used in systems such as the submerged-arc furnace to evaluate the total current passing through the charge material as well as the current distribution in various regions of the furnace. Experiments were carried out to measure the current passing through liquid slag as a function of the dimensions of the electrode, geometry of the system, applied voltage, height of the slag column and the depth of immersion of the electrode in the slag. There was good agreement between the predictions of the shell model and the experimental observations. The model also successfully predicts the minimum height of the slag column required for sustaining resistance heating and also the influence of current on the erosion of the electrode.