The Diode–Resistor Circuit: A Simple Circuit with No Elementary Solution

In this paper, the author will discuss the diode–resistor circuit and how such a simple circuit with only two components has no analytical solution in terms of standard elementary functions. Furthermore, the author will introduce a novel approximate solution for the problem in terms of elementary functions for practical applications. The derivation will only rely on algebraic manipulations and some properties of elementary functions. The paper will be of interest for undergraduate students as well as general physics instructors.