Relationships are derived which describe the voltage of and the ionic and electronic currents through a solid electrolyte galvanic cell under load as an explicit function of the independent variables. These relationships result from an appropriate extension of the classical Wagner approach for the open circuit case to the conditions of a cell in charge or discharge mode. The formulae represent generalized versions of the Wagner-Schmalzried equations. They readily allow determination of the chemical potential distribution throughout the electrolyte under load conditions.