Energy Losses in Charging and Discharging of Capacitors

Analytical expressions are derived for the energy loss incurred in charging and discharging of lossy, i.e. dispersive capacitors under nearly step-function voltage, such as might be expected in the presence of a finite series resistance and with step-function rise and fall of the voltage. It is shown that the energy loss in the process of charging and discharging may amount to a large fraction of the total stored energy in the capacitor and this may give rise to a significant amount of heating. A physically realistic characteristic function is assumed for the capacitor, corresponding to a frequency-independent pendent loss over a large range of frequencies, such as might be obtained in many low-loss materials.