Resolution of circuits from a physical point of view.

Abstract

The resolution of electrical circuits and its acoustic homologous from a physical point of view is presented here. Based on the structural analogy with a mechanical system in equilibrium, it is possible to associate a Lagrangian depending on the generalized forces in a viscous medium with friction coefficients and with a set of holonomic constraint functions. By means of the Hamilton principle applied to this Lagrangian associated with a circuit, an equation of a function of a set of independent variables can be obtained, which turns out to be the condition for the resolution of a typical problem of linear programming. This minimized expression represents, in turn, the power dissipation. From all the possible values that could take a set of speed and pressure, the principle picks out one and only one (the true values) with the condition of producing the least power dissipation. All acoustic devices or systems that could be represented by an electric circuit may be solved by this method with the physical meaning described here.