Abstract
The Lagrangian and Hamiltonian for series RLC circuit has been formulated. We use the analogical concept of classical mechanics with electrical quantity. The analogy is as follow mass, position, spring constant, velocity, and damping constant corresponding with inductance, charge, the reciprocal of capacitance, electric current, and resistance respectively. We find the Lagrangian for the LC, RL, RC, and RLC circuit by using the analogy and find the kinetic and potential energy. First, we formulate the Lagrangian of the system. Second, we construct the Hamiltonian of the system by using the Legendre transformation of the Lagrangian. The results indicate that the Hamiltonian is the total energy of the system which means the equation of constraints is time independent. In addition, the Hamiltonian of overdamping and critical damping oscillation is distinguished by a certain factor.
Highlights
Lagrangian and Hamiltonian are topics part of analytical mechanics or classical mechanicscourse that s studied in the second or third year of the undergradute physics program.Some advantages are obtained when using Lagrangian and Hamiltonian formalismto solve the mechanical problems
This research aims to formulate the Hamiltonian extension for the series RLC circuit without emf source, which is the simple case
LC Circuit To formulate the Lagrangian, first, we have to solve the differential equation of Kirchhoffs rule for series LC circuit without emf source as follow which has a solution for discharging capacitor (2)
Summary
Lagrangian and Hamiltonian are topics part of analytical mechanics or classical mechanicscourse that s studied in the second or third year of the undergradute physics program.Some advantages are obtained when using Lagrangian and Hamiltonian formalismto solve the mechanical problems. The problem discussed in physics textbooks about the properties of electric currents and the potential difference or voltage that are in the electronic devices on the circuit [2]. The RLC circuit becomes an example in the differential equations subtopics in the mathematical physics course [3]. The RLC circuit is limited to the topic of electricity or solving differential equations. Current RLC research is heading toward the quantum level. This is due to the rapid development of nanotechnology so that nanosized electronic devices are being developed. The quantum mechanics of the RLC circuit which obtained the approximation of energy eigenvalues in terms of a dimensionless parameter has been studied [5]
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