  While the standard (introductory physics) way of computing the equvalent
resistance of non-trivial electrical ciruits is based on Kirchhoff's rules,
there is a mathematically and conceptually simpler approach, called the method
of nodal potentials, whose basic variables are the values of electric potential
at the circuit's nodes.
  In this paper, we review the method of nodal potentials and illustrate it
using the Wheatstone bridge as an example. At the end, we derive - in a closed
form - the equivalent resistance of a generic circuit, which we apply to a few
sample circuits. The final result unveils a curious interplay between
electrical circuits, matrix algebra, and graph theory and its applications to
computer science. The paper is written at a level accessible by undergraduate
students who are familiar with matrix arithmetic. For the more inquisitive
reader, additional proofs and technical details are provided in the appendix.
