Analyzing the Response Current of a Series RL Circuit Using Graphic

Abstract

This study presents a MATLAB-based graphical approach for analysing the transient current response of a series resistor-inductor (RL) circuit. It focuses on decomposing the total current into natural-response and forced-response components under specified circuit parameters. Resistance, inductance and the electrical angle of the power-supply voltage are treated as key variables. The complete response-current expression for the first-order circuit equation is derived, and the natural, forced and complete response-current values are calculated and plotted in MATLAB. Rather than relying only on algebraic calculation, the work emphasises the simultaneous display of the natural, forced and complete current curves. Several verification cases demonstrate how changes in supply voltage and angular input affect the resulting current waveforms. An additional protection-relay example illustrates the practical relevance of the method for power-system transient analysis. The results indicate that graphical representation can clarify the behaviour of transient current components in a series RL circuit and support comparison between calculated values and plotted waveforms. The proposed MATLAB procedure offers a simple instructional tool for visualising response-current characteristics and examining the effect of circuit parameters on transient behaviour. The study is intended mainly for educational and explanatory purposes, particularly for readers seeking to understand the relationship between analytical calculation and graphical representation in basic RL circuit analysis.