The genesis of the internal resistance of a battery -- a physical perspective

TL;DR

This paper provides a physical explanation for the internal resistance of batteries, showing it arises from the fundamental relationship between chemical potential and terminal voltage during current flow.

Contribution

It offers a logical derivation of internal resistance based on chemical potential differences, challenging the traditional view as merely experimental.

Findings

Internal resistance is necessary for battery operation.

Linear relation between current and voltage change for small variations.

Thevenin's theorem presupposes the derived physical principles.

Abstract

The standard exposition of the internal resistance of a battery, that a battery comprises a source of emf in series with an internal resistance, as given in engineering and physics text-books, is lacking in proper explanation. It is treated merely as an experimental fact, and not something that should follow from logic. The battery has a tendency to maintain electric potential difference across its terminals equal to its chemical potential, and in an open circuit, when no current flows, these two do match. However in a closed circuit, a drop in electric potential across the battery terminals is inevitable for a steady flow of electric current throughout the circuit, because the chemical reactions driving the electric current within the battery can proceed only if the electric potential at its terminals differs from the chemical potential. It is shown that for small voltage changes, the current passing through the battery is linearly proportional to the change in potential from the open-circuit value (i.e., its chemical potential), giving rise to a semblance of an internal resistance in series with the external resistance. It follows that a battery {\em has to have} an internal resistance in order to function as a power source. It is also shown that Thevenin's theorem does not make our results superfluous, in fact our results are presupposed in its derivation.