  Direct current (DC) circuits are usually taught in upper-level physics
curricula, and Kirchhoff's laws are stated and used to solve the steady-state
currents. However, students are not often introduced to alternative techniques,
such as variational principles, for solving circuits. Many authors have tried
to derive the steady-state distribution of currents in circuits from
variational principles, and the initial attempts were carried out by great
physicists, such as Kirchhoff, Maxwell and Feynman. In this article, we shall
review such variational principles in physics and illustrate how they can be
used to solve DC circuits. We will also explore how they are related, in a
fundamental way, to the entropy production principles of irreversible
thermodynamics. We believe that the introduction of variational alternatives
for solving circuits can be a good opportunity for the instructor to present
the techniques of the calculus of variations and irreversible thermodynamics to
students.
