Process for manufacturing a power cable includes: providing a power cable core having an electric conductor; providing a copper foil; providing a protective strip over the power cable core, the protective strip having a radially inner and outer surface and being made of copper with a coating; folding the copper foil around the power cable core so as to bring two longitudinal copper foil rims to contact one to the other; welding the two contacted longitudinal copper foil rims thus obtaining a copper sheath in form of a tube with a welding seam; reducing the diameter of the copper sheath to put it into direct contact with the power cable core and the protective strip; heating the protective strip and the copper sheath at a temperature higher than the melting temperature of the coating of the strip so that the coating fuses in the welding seam.