Transient and Steady Current in a Series RL Circuit

Part of electrical engineering is circuit theory, which includes methods for calculating steady and transient currents in a series RL circuit. Power systems are typically inductive and can be modeled with RL circuits. An RL circuit is formed by a real voltage source, 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. Current in a series RL circuit is the solution to an ordinary differential equation, which is a mathematical expression of Kirchhoff’s voltage law. The goal is the maximum possible reduction of mathematical manipulations in solving the equation for current calculation. Methods for solving the equation in a series RL circuit was proposed. In contrast to the literature, neither the phasor technique, the Fourier circuit analysis, the Laplace transform nor the convolution integral technique is used in the calculation of current. A mathematically correct solution to the equation is supplemented with solutions of illustrative examples. This solution is confronted with solution methods in electrical engineering and physics textbooks. The importance of the initial condition of current whose first derivative occurs in the equation is emphasized. An original definition of steady current and transient current is proposed.