Ecuaciones en Diferencias Finitas Parciales en Mallas Eléctricas
AbstractThis paper presents a method to analyze a triangular network of equal electrical impedances, and composed by triangular meshes constituted themselves by these impedances; and shows how to obtain a partial, finite differences equation, relating the Maxwell current in each mesh (n,m) with those currents in the currents in the neighboring meshes. The differences equation is solved by the method of Lagrange, and boundary conditions are applied in order to obtain explicitly the total, equivalent impedance of the network and the distribution of the Maxwell currents across thew hole network. This treatment surpasses the usual one of isolating meshes and nodes, applying the two laws of Kirchhoff tocurrents and voltages and finally solving a large system of linear algebraic equations by numerical or algebraic methods. During many years as an electrical engineer, the author has not seen used this methodology, so that he considers this is an original and useful addition to the theory of electric circuits.
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