  We investigate currents in a quantum ring threaded by a magnetic flux which
can be varied in an arbitrary way from an initial value $\phi_i$ at time $t_i$
to a final value $\phi_f$ at time $t_f$. Dynamics of electrons in the ring is
described by the Hubbard and the extended Hubbard models. We demonstrate that
time dependence of the induced current bears information on electron
correlations. In the case of the Hubbard model with infinite on--site repulsion
we prove that the current for $t>t_f$ is independent of the flux variation
before $t_f$. Additionally, this current is fully determined by a solution of
the initial equilibrium problem and the value of $\phi_f$. Apart from
mesoscopic rings our results pose important implications for designing of
quantum motors built out as the ring--shaped optical lattice.
