This work aims to evaluate the electrical conductivity and the rheological and mechanical properties of copolymer/carbon black (CB) conductive polymer composites (CPCs). The copolymers, containing ethylene groups in their structure, used as matrix were polyethylene grafted with maleic anhydride (PEgMA), ethylene‐methyl acrylate–glycidyl methacrylate (EMA‐GMA), and ethylene‐vinyl acetate (EVA). For comparison purposes, bio‐based polyethylene (BioPE)/CB composites were also studied. The electrical conductivity results showed that the electrical percolation threshold of BioPE/CB composite was 0.36 volume fraction of CB, whereas the rheological percolation threshold was 0.25 volume fraction of CB. The most conductive CPC was BioPE/CB. Among the copolymer/CB CPCs, PEgMA/CB showed the highest conductivity, which can be attributed to the fact that the PEgMA copolymer had higher crystallinity. It also has a higher amount of ethylene groups in its structure. Torque rheometry analysis indicated that EMA‐GMA copolymer may have reacted with CB. Rheological measurements under oscillatory shear flow indicated the formation of a percolated network in BioPE/CB and copolymer/CB composites. Morphology analysis by scanning electron microscopy (SEM) indicated the formation of a percolated network structure in BioPE/CB composite and finely dispersed CB particles within the PEgMA copolymer. Wetting of CB particles/agglomerates by the copolymer matrix was observed in EVA/CB and EMA‐GMA/CB composites. Conductive CB acted as reinforcing filler as it increased the elastic modulus and tensile strength of BioPE and the copolymers.