Transient and steady currents in a parallel RL circuit

Abstract

Part of electrical engineering is circuit theory, which includes methods for calculating steady and transient currents in a parallel RL circuit. Power systems are typically inductive and can be modelled with RL circuits. The proposed methods can be used in the calculation of short-circuit currents and in the calculation of current density in solid conductors that form transmission lines. An RL circuit is formed by real voltage sources, inductors and resistors. The inductance and resistance of the circuit elements do not depend on time. The ideal voltage source, which is part of the real source, has voltage depending on time. Currents in a parallel RL circuit are solutions to ordinary differential and algebraic equations, which are mathematical expressions of Kirchhoff's laws. The original contribution of this paper is the derivation of equations for the calculation of currents in a circuit for all possible combinations of circuit elements. The importance of the initial conditions of currents whose first derivative occurs in the equations is emphasized. An original definition of steady current and transient current is proposed. The theory is supplemented with solutions of illustrative examples.Part of electrical engineering is circuit theory, which includes methods for calculating steady and transient currents in a parallel RL circuit. Power systems are typically inductive and can be modelled with RL circuits. The proposed methods can be used in the calculation of short-circuit currents and in the calculation of current density in solid conductors that form transmission lines. An RL circuit is formed by real voltage sources, inductors and resistors. The inductance and resistance of the circuit elements do not depend on time. The ideal voltage source, which is part of the real source, has voltage depending on time. Currents in a parallel RL circuit are solutions to ordinary differential and algebraic equations, which are mathematical expressions of Kirchhoff's laws. The original contribution of this paper is the derivation of equations for the calculation of currents in a circuit for all possible combinations of circuit elements. The importance of the initial conditions of currents whose first derivative occurs in the equations is emphasized. An original definition of steady current and transient current is proposed. The theory is supplemented with solutions of illustrative examples.