  We report on measurements of the electrical conductivity in both a 2D
triangular lattice of metallic beads and in a chain of beads. The
voltage/current characteristics are qualitatively similar in both experiments.
At low applied current, the voltage is found to increase logarithmically in a
good agreement with a model of widely distributed resistances in series. At
high enough current, the voltage saturates due to the local welding of
microcontacts between beads. The frequency dependence of the saturation voltage
gives an estimate of the size of these welded microcontacts. The DC value of
the saturation voltage (~ 0.4 V per contact) gives an indirect measure of the
number of welded contact carrying the current within the 2D lattice. Also, a
new measurement technique provides a map of the current paths within the 2D
lattice of beads. For an isotropic compression of the 2D granular medium, the
current paths are localized in few discrete linear paths. This
quasi-onedimensional nature of the electrical conductivity thus explains the
similarity between the characteristics in the 1D and 2D systems.
