Abstract: A charging system employing a liquid-cooled transmission cable for transferring power. The transmission cable has a central tube with an extruded member disposed therewithin for carrying coolant. A plurality of layers of coaxial tubular wire braid are disposed around the central tube that carry charging current and that are separated by a layers of dielectric material. An outer layer of wire braid is disposed around an outermost layer of dielectric material that is used for grounding and/or shielding. An outer jacket is disposed around the outer layer of wire braid for encasing the transmission cable. The extruded member may comprise a thermoplastic rubber extrusion, for example. The coolant path through the transmission cable is internally supported by means of the extruded member to assure uniform flexibility, maintain tangential magnetic flux, and eliminate kinking and collapse of the flow path.