  The non-equilibrium properties of a driven quasi-one dimensional
superconducting ring subjected to a constant electromotive force ({\it emf}) is
studied. The {\it emf} accelerates the superconducting electrons until the
critical current is reached and a dissipative phase slip occurs that lowers the
current. The phase slip phenomena is examined as a function of the strength of
the {\it emf}, thermal noise, and normal state resistivity. Numerical and
analytic methods are used to make detailed predictions for the magnitude of
phase slips and subsequent dissipation.
