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.
Highlights
Lagrangian formalism is a powerful way to obtain the equation of motion of a physical system
In the mathematical physics subject, the RLC circuit is commonly used to show the application of differential equation in the physical system [4]
We found most analysis of the RC, RL, LC, and RLC circuits, as a mesoscopic system or nanophysics, are commonly discussed and formulated by using the concept of quantum mechanics [7,8,9,10]
Summary
Lagrangian formalism is a powerful way to obtain the equation of motion of a physical system. We know that we can formulate the physical system in form of Lagrangian defined as the kinetic energy minus potential energy of the physical system. We formulate the Lagrangian for LC, RC, RL, and RLC circuits by using the analogy with the classical mechanics formulation for a physical system. The solution of the differential equation of Eq (1) with the initial condition q(0) = 0 is not relevant to the physical reality it is possible from the mathematics point of view. To formulate the lagrangian of a physical system, we must know the potential energy and kinetic energy of the system. To formulate the kinetic energy of the RL circuit, we use the analogy concept by using the usual mechanical kinetic energy 1⁄2 mv and electric current I correspond with velocity v, and we have. There are three possible cases for the parameter i.e. overdamping, critical damping and underdamping
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