We report on measurements of the electrical conductivity in both a 2D triangular lattice of metallic beads and in a chain of beads. In both experiments, the voltage is found to increase logarithmically with the low applied current 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 a hint on the size of these welded microcontacts. The DC value of the saturation voltage ($\simeq 0.4$ V per contact) gives a measurement of the number of welded contact carrying the current within the 2D lattice. A new measurement technique gives also access to the cartography of the current paths within the 2D lattice of beads. Both the model and the cartography show the quasi-unidimensionnal feature of the electrical conductivity in such a 2D system. For both systems, the dissipated power drives the irreversibility threshold of the voltage/current characteristics. At very low current, the characteristics are found to be non linear, the non linear part of the current being a universal power law of the voltage.