Active charge and discharge of a capacitor: Scaling solution and energy optimization
Résumé
We study—both theoretically and experimentally—charging and discharging capacitors that are actively controlled using a voltage source. We show how an appropriate choice of control voltage allows the charging or discharging to take place very slowly (quasistatically). Conversely, we study the price to be paid in terms of Joule heat when we speed up these processes. Finally, we develop optimal processes that minimize energy consumption for a finite charging time. Our study combines fundamental concepts in thermodynamics, classical mechanics, and electrical circuits. This topic lends itself well to an experimental project in the classroom, involving computer control of a voltage source, data acquisition, and processing.