Differential equations for the resolution of LRC electrical circuit
DOI:
https://doi.org/10.5902/2179460X40515Keywords:
Differential equations, Electrical circuits, Analytical methodsAbstract
Studies about differential equations provide many mathematical instruments that aid the insight of many practical problems. The goal of this paper is to obtain a differential equation that describes an Electrical Engineering problem, then to define the solution of this equation using analytical methods and to compare theoretical and experimental results. Firstly, the second order differential equation with constant coefficients and the analytical method to obtain the respective solution will be studied; later this solution will be applied in the problem of an LRC electrical circuit with simple mesh with an inductor (L), a resistor (R), a capacitor (C) and an electromotive source. The goal is to solve the differential equation to define the charge, in function of the time, between the capacitor and the inductor. The solution is obtained from the homogeneous solution (admitting a solution in the exponential form) and the particular solution (using the undetermined coefficients method, due to function form). Initial conditions for the initial charge and the initial current can be used, with the analytical methods, to find the particular solution of the problem.
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BOYCE, William E.; DIPRIMA, Richard C. Equações diferenciais elementares e problemas de valores de contorno. Tradução Valéria de Magalhães Iorio. 10. ed. Rio de Janeiro: LTC, 2015.
HALLIDAY, David; RESNICK, Robert. Fundamentos de Física: volume 3. Tradução Ronaldo Sérgio de Biasi. 9. ed. Rio de Janeiro: LTC, 2012.
NILSSON, James W. Circuitos Elétricos: volume 1. Tradução Sonia Midori Yamamoto. 10. ed. São Paulo: Pearson Education do Brasil, 2015.
ZILL, Dennis G.; CULLEN, Michael R. Equações Diferenciais: volume 1. Tradução Antonio Zumpano. 3. ed. São Paulo: Pearson Makron Books, 2001.
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