Beyond Fragmented Instruction: A Physico-Mathematical Approach to Teaching Electric Circuit Theory in Higher Education

Abstract

Traditional introductory electric circuit theory courses in university engineering programs frequently segment direct current (DC) and alternating current (AC) regimes into isolated pedagogical modules. This curricular fragmentation conceals the underlying electromagnetic principles and energy transfer dynamics, encouraging students to rely on fragmented, rule-based algorithm execution rather than developing a unified conceptual framework. This paper proposes an integrated physico-mathematical pedagogical model designed to reconcile DC, transient, and AC steady-state regimes within a continuous analytical framework. By leveraging energy conservation principles, foundational differential and integral constitutive relations, phasor representations, and numerical techniques (e.g., Runge-Kutta), DC is reframed as the zero-frequency limiting case of dynamic AC signals rather than a distinct physical phenomenon. The proposed instructional sequence synergizes predictive conceptual reasoning, active computational simulation, and empirical laboratory verification to address well-documented student learning difficulties—such as local reasoning, sequential current consumption, and misinterpretations of reactive power and phase shifts. This comprehensive approach shifts the educational paradigm from passive algorithmic memorization toward robust scientific modeling, enhancing knowledge transfer across complex electrical configurations and non-sinusoidal excitations.