Surfactants such as Aerosol OT (AOT) are commonly used to stabilize and electrically charge nonpolar colloids in devices such as electronic ink displays. The electrical behavior of such devices is strongly influenced by the presence of charged inverse micelles, formed by excess surfactant that does not cover the particles. The presence of charged inverse micelles results in increased conductivity of the solution, affecting both the energy consumption of the device and its switching characteristics. In this work, we use transient current measurements to investigate the electrical properties of suspensions of the surfactant Aerosol OT in dodecane. No particles are added, to isolate the effect of excess surfactant. The measured currents upon application of a voltage step are found to be exponentially decaying, and can be described by an analytical model based on an equivalent electric circuit. This behavior is physically interpreted, first by the high generation rate of charged inverse micelles giving the suspension resistor like properties, and second by the buildup of layers of charged inverse micelles at both electrodes, acting as capacitors. The model explains the measurements over a large range of surfactant concentrations, applied voltages, and device thicknesses.