Lagrangian for RLC circuits using analogy with the classical mechanics concepts

TL;DR

This paper formulates the Lagrangian for various RLC circuits by drawing an analogy with classical mechanics, revealing how different circuit types correspond to energy-like terms.

Contribution

It introduces a systematic approach to derive Lagrangians for RLC circuits using classical mechanics analogies, clarifying their energy contributions.

Findings

LC and RLC circuits have kinetic and potential energy-like terms in their Lagrangians.

RC circuit's Lagrangian is solely potential energy-like.

RL circuit's Lagrangian is solely kinetic energy-like.

Abstract

We study and formulate the Lagrangian for the LC, RC, RL, and RLC circuits by using the analogy concept with the mechanical problem in classical mechanics formulations. We found that the Lagrangian for the LC and RLC circuits are governed by two terms i. e. kinetic energy-like and potential energy-like terms. The Lagrangian for the RC circuit is only a contribution from the potential energy-like term and the Lagrangian for the RL circuit is only from the kinetic energy-like term.