Theoretical and experimental investigation of optimal capacitor charging process in RC circuit

Abstract

The problem of optimal capacitor charging in a RC circuit is investigated using finite-time thermodynamics (FTT). Both the resistor and the capacitor are assumed to be nonlinear, and the optimal time paths of source voltage for the minimum charging time and the minimum Joule heat dissipation are obtained by using optimal control theory, respectively. The optimal time path of source voltage is also compared with the classical strategies of constant source voltage and linear source voltage operations. The results show that the optimal time path of source voltage for the minimum charging time consists of the initial and final instantaneous voltage change and the middle maximum admissable constant-voltage branches, which is independent of the nonlinear characteristics of both the resistor and the capacitor; when the ratio of the time constant of the circuit to the charging time is relatively smaller, the charging strategy of linear electric-source voltage is much closer to the optimal time path of the source voltage of the minimum Joule heat dissipation, while, when the ratio of the time constant of the circuit to the charging time is relatively larger, the charging strategy of constant source voltage is much closer to the optimal time path of source voltage of the minimum Joule heat dissipation; when the resistance is constant, the voltage difference between the source and the capacitor for the minimum Joule heat dissipation of the process is always a constant whether the capacitor is linear or nonlinear, and this conclusion is also valid for the case with the current law of “function of difference”. An experiment of capacitor charging processes in the RC circuit is performed finally, and the results show that real voltage profiles of the resistor for different charging strategies are consistent with the corresponding results of theoretical analysis.