The maximum work output of an electric battery in a given time

A new model of an electric battery is established, based on the simplest battery model and Denno's battery model with an internal dissipation. The model is used to investigate the fundamental problem of how to maximize the work output of an electric battery in a given time. The important relation of the voltage across the battery terminals varying with the discharging time is derived by using variational calculus. The maximum work output of the battery is calculated. The optimal matching condition of the load resistance is determined. The reasonable range of the discharging time is given. The other characteristics of the battery at the maximum work output are discussed further. The results obtained here have some theoretical applications not only for raising the utilization of the electric energy stored in batteries, but also for improving the performance of some electric circuits.