In this work we present a complete study of the electrical conductivity evolution of molten nano-composites under extensional deformation. The conductive polymer composites are a pure Polystyrene matrix filled with Carbon Nanotubes. The conductivity properties of the composites rely on the formation of a percolated network through the material. When the composite flows, the filler network can be disrupted, altering the conductivity of the composite. Thus, after a small deformation a moderately conductive composite can turn into an insulating material. From an applied viewpoint, for instance, the thermoforming of a composite sheet with good electrical properties can lead to an insulating finished part. In the literature, the studies mainly focus on the conductivity variation of molten composites under small shear deformation at low shear rates.This study aims at analyzing the microstructure evolution when the molten composite undergoes large deformation and especially in elongation. That is why we developed a new experiment that gives the possibility to monitor the specimen conductivity during its extensional deformation all the while recording the elongation stress. On the one hand, we highlighted a close relationship between the extensional conditions that are the specimen temperature and the extensional rate with the conductivity variation. Indeed, the conductivity variations can be described by means of the Weissenberg number that takes into account the polymer dynamics and the extensional rate. On the other hand, we have shown that the volume confinement of the filler, here achieved by the presence of polybutadiene nodules, gives the possibility to decrease the filler amount without impacting the process-ability of the composites. Finally, we propose a model that describes the conductivity evolution of CPC under extensional and planar flow. It links the structural evolution of the filler network to the macroscopic properties of the composite