We consider random resistor networks with nodes given by a simple point process on R d and with random conductances. The length range of the electrical filaments can be unbounded. We assume that the randomness is stationary and ergodic w.r.t. the action of the group G, given by R d or Z d . This action is covariant w.r.t. the action of G by translations on the Euclidean space. Under very basic and minimal assumptions we prove that a.s. the suitably rescaled directional conductivity of the resistor network along the principal directions of the effective homogenized matrix D converges to the corresponding eigenvalue of D times the intensity of the simple point process. The above result covers plenty of models including e.g. the standard conductance model on Z d (for which we improve the existing results), the Miller-Abrahams resistor network for conduction in amorphous solids (to which we can now extend the bounds in agreement with Mott's law previously obtained in [8,19,20] for Mott's random walk), resistor networks on the supercritical cluster in lattice and continuous percolations (solving an open problem for Bernoulli supercritical percolation on Z d ), resistor networks on crystal lattices and on Delaunay triangulations.