Active charge and discharge of a capacitor: scaling solution and energy optimization

TL;DR

This paper investigates the energy dynamics of actively charging and discharging capacitors, deriving optimal control strategies to minimize energy loss and exploring the thermodynamic and mechanical principles involved.

Contribution

It introduces a combined theoretical and experimental approach to optimize capacitor charging processes, bridging thermodynamics, mechanics, and electrical engineering.

Findings

Quasistatic charging minimizes Joule heat.

Faster charging increases energy dissipation.

Optimal protocols reduce energy consumption for finite times.

Abstract

Capacitors are ubiquitous in electronic and electrical devices. In this article, we study -- both theoretically and experimentally -- the charging and discharging of capacitors using active control of a voltage source. The energy of these processes is analyzed in terms of work and heat. We show how to approach the quasistatic regime by slowing down the charging or discharging processes. 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 work combines fundamental concepts from thermodynamics, classical mechanics and electrical circuits, thus blurring the artificial frontiers at the undergraduate level between these disciplines. Also, it provides a simple example of a prominent problem in current science, the optimization of energy resources. Moreover, our study lends itself well to an experimental project in the classroom, involving computer control of a voltage source, data acquisition, and processing.