The Relational Ohm's Law Analogy: A Pedagogical Bridge from Circuits to Cosmology

This paper presents a pedagogical framework that uses Ohm’s Law and impedance geometry as a universal teaching bridge for understanding coupled systems across disciplines. By framing complex interactions in terms of push, flow, and constraint, the approach leverages students’ existing intuition from circuit theory to build transferable understanding of abstract information-coupling structures. Key quantitative elements of circuit theory—parallel channel division, phase angle, reactive fraction, bandwidth, and quality factor—are shown to form a coherent geometric language for describing two-channel systems. In particular, bounded diagnostics such as phase angles replace unbounded ratios, enabling scale-independent comparison across systems. The familiar behavior of AC circuits provides concrete examples of how balance points, efficiency, and resonance naturally emerge from impedance relationships. The framework is explicitly pedagogical rather than physical: it does not claim that systems outside electronics obey circuit laws, nor that constants arise from electrical equations. Instead, it demonstrates that impedance geometry provides a shared mathematical grammar that appears in many domains, making it a powerful tool for teaching, communication, and interdisciplinary transfer. By emphasizing structural homology over physical identity, this approach equips students, educators, and researchers with a clear, quantitative, and intuitive method for reasoning about complex coupled systems—one that can be taught forward, adapted across fields, and used without commitment to any specific theoretical framework.