The persistent current for an arbitrarily filled strongly interacting one-dimensional ring is studied using variational and numerical exact diagonalization methods. For an ordered ring a difference between the commensurate and the incommensurate cases is observed. While for the commensurate case the current in the limit of strong interactions always tends to zero, in the incommensurate case there are situations (termed the frustrated cases) in which the current is finite. For a disordered ring the current always tends to zero in the limit of strong interactions. The implications on persistent current experiments are discussed.
