A Unified Analytical Framework for Geometry-Dependent Resistance and Power Loss in Electrical Conductors

Efficient electrical conductor design is a critical factor in minimizing resistive power dissipation in modern electrical and electronic systems, particularly in compact devices, flexible circuits, and thermally constrained architectures. Conventional electrical conduction theory describes current transport through the fundamental relations of Ohm’s Law and the resistive formulation R=ρL/A, which relate electrical resistance to conductor material properties and geometric dimensions. However, practical conductor performance in real systems often deviates from ideal conditions due to geometric deformation, conductor routing constraints, thermal variation, and imperfect electrical contacts. This study proposes a geometry-aware conductor design model that extends the classical resistance formulation into an engineering framework capable of estimating resistive power loss reduction under redesigned wire configurations. The proposed formulation introduces an effective resistance representation that incorporates geometric curvature density, twisting or folding density, effective conductor length, temperature variation, and contact-quality parameters. By integrating these design-dependent variables into a unified analytical structure, the model enables systematic evaluation of geometry-induced variations in conductor resistance and associated Joule heating losses. The framework further introduces a loss-reduction metric that quantifies the percentage reduction in resistive power dissipation between conventional and optimized conductor designs. Analytical evaluation demonstrates that improvements in conductor radius, reduction in effective routing length, enhanced thermal conditions, and improved electrical contact quality can collectively contribute to measurable reductions in resistive losses. Such reductions are particularly relevant in applications where conductor geometry must adapt to spatial constraints, including flexible electronics, wearable electrical systems, high-density circuit interconnections, and compact power distribution networks. Importantly, the proposed model does not introduce a new fundamental electrical law. Instead, it provides a design-oriented extension of established conductor physics, enabling the integration of geometric and environmental factors into practical resistance estimation. By bridging classical electrical theory with engineering design parameters, the framework offers a structured analytical tool for conductor optimization and comparative performance analysis in real-world electrical systems. The proposed geometry-aware model therefore provides a foundation for future experimental validation, numerical simulation, and application-specific conductor optimization studies aimed at reducing resistive losses and improving electrical energy efficiency in modern wiring architectures. Please check the attachment for details