Analysis of Multi-Loop Electrical Circuits Using Gaussian Elimination and Gauss-Jordan Methods on MATLAB Platform

Abstract

Multi-loop electrical circuit analysis represents a significant challenge in electrical engineering that requires solving complex linear equation systems. This research aims to evaluate the effectiveness of Gaussian Elimination and Gauss-Jordan methods in solving linear equation systems generated from multi-loop electrical circuit analysis using MATLAB platform. The study employs a descriptive quantitative approach by analyzing a 3-loop circuit consisting of six resistors  and three voltage sources (V₁ = 8V, V₂ = 4V, V₃ = 12V). The application of Kirchhoff's laws generates a 3×3 linear equation system that is solved using both elimination methods. MATLAB implementation demonstrates that both methods produce identical solutions with current values I₁ = 2.695A, I₂ = 2.043A, and I₃ = 1.560A. The Gaussian Elimination method is more efficient for small to medium systems as it only requires forward elimination and back substitution, while the Gauss-Jordan method offers better solution transparency by forming a reduced row echelon form (RREF) matrix that allows direct solution reading without additional substitution processes. Implementation on the MATLAB platform provides significant advantages in terms of computational efficiency, calculation accuracy, and ease of result visualization. This research proves that both methods can be effectively applied to electrical circuits with high complexity levels and provides important contributions to the development of multi-loop electrical circuit analysis methods with systematic and structured numerical approaches.