  An approach by Stephen is used to investigate the critical properties of
randomly diluted resistor networks near the percolation threshold by means of
renormalized field theory. We reformulate an existing field theory by Harris
and Lubensky. By a decomposition of the principal Feynman diagrams we obtain a
type of diagrams which again can be interpreted as resistor networks. This new
interpretation provides for an alternative way of evaluating the Feynman
diagrams for random resistor networks. We calculate the resistance crossover
exponent $\phi$ up to second order in $\epsilon=6-d$, where $d$ is the spatial
dimension. Our result $\phi=1+\epsilon /42 +4\epsilon^2 /3087$ verifies a
previous calculation by Lubensky and Wang, which itself was based on the
Potts--model formulation of the random resistor network.
