Electrical Networks
Nathan Albin, Pietro Poggi‐Corradini · 2025
Here we describe the theory of electrical current flows as unit flows that minimize energy giving rise to the Cycle Law and Ohm&s;s Law. We then study the harmonicity of voltage potentials and develop the Maximum Principle. Finally, we introduce the notion of effective resistance. We recall the Serial rule and the Parallel rule, as well as the metric properties of effective resistance. Then, we conclude by presenting the linear-algebraic approach culminating with the Dirichlet and Thomson principles.