To simplify electric connection, connectors (200) have been developed in which the connection interface to the switchgear units is flat, and the connecting end-piece (220) is standardized and forms a rigid shell (222). The connector (200) comprises a conducting insert (210) in an over-moulded compressible insulating elastomer (204). The connection surfaces of the conducting insert (204) of the connection device (202) to the apparatuses are laid back with respect to the connection surfaces of the insulating support (204). When connection is performed with another device modified in similar manner, the insulating surfaces come into contact, and compression is then performed enabling the interface to be tightly sealed, while at the same time bringing the conducting surfaces into contact. To achieve a tight embedding between the conducting insert (224), the deformable insulating support (226) and the standardized rigid shell (220), the dimensions and internal shapes are adapted accordingly.