The invention is an inductive device featuring very low losses even in circuits that supply more than about 10 kilowatts of power. The device includes an inductor comprising a core (300) consisting primarily of a highly permeable magnetic material and at least one winding (304) of a high temperature superconducting conductor contained substantially within the core (300) and in spaced relation with respect to the core (300) sufficient to maintain its electrical integrity, a refrigeration means for cryogenically cooling at least the conductor winding portion (304) of the inductor to a temperature at which each conductor winding (304) exhibits superconductivity, and an input/output device for providing power to and receiving power from each conductor winding (304). Also disclosed are a balancing choke and a circuit embodying a common mode inductor made in accordance with the invention.