Application of Adiabatic Process for Decreasing Energy Loss in Discharging A Capacitor

This paper presents an application of adiabatic technique to the process of discharging a capacitor in an RC circuit. In such a process, a fully charged capacitor is allowed to release its stored charge through an arbitrary number of steps. Each step is controlled by including a battery whose voltage is less than, and opposite in polarity to the voltage on the capacitor. Theoretical derivation of the heat energy dissipated in the resistor and the energy gained by the battery is presented and analyzed. It is shown that the dissipated heat energy decreases as the step number increases but constant across all steps. Our results also show that the initial energy stored in the capacitor is distributed as heat energy and energy gained by the battery. Moreover, as the step number increases, the energy gain by the battery increases and the heat energy decreases and in the limit as the number of steps approaches infinity the heat energy vanishes and thus all the initial energy in the capacitor has been gained by the battery. In addition, our theoretical adiabatic method is tested experimentally and consistent results are obtained. This method of adiabatic discharging for large N recovers up to 99% of the stored energy, offering applications in regenerative braking and energy harvesting systems.