An electrical connecting device having a main body and a displacement body mounted in a linearly movable manner relative to one another in a longitudinal direction. The main body has a cavity that accommodates a longitudinal section of the displacement body or vice versa. The length of the longitudinal section accommodated in the cavity is variable by a relative longitudinal movement of the main body and the displacement body. The main body has conductor tracks extending in the longitudinal direction and insulated from one another. The displacement body has sliding elements insulated from one another and resting on and electrically contacting a contact surface of a respective one of the conductor tracks. The conductor tracks are arranged on a main body surface of the main body. The main body surface is round in a cross-sectional plane perpendicular to the longitudinal direction or is formed by a plurality of surface sections angled in relation to one another. The sliding elements project from a displacement body surface of the displacement body. The displacement body surface is round in the cross-sectional plane or is formed by a plurality of surface sections angled in relation to one another. The contact surfaces of at least two of the conductor tracks are angled in relation to one another.