  We thoroughly study the persistent current of noninteracting electrons in
one, two, and three dimensional thin rings. We find that the results for
noninteracting electrons are more relevant for individual mesoscopic rings than
hitherto appreciated. The current is averaged over all configurations of the
disorder, whose amount is varied from zero up to the diffusive limit, keeping
the product of the Fermi wave number and the ring's circumference constant.
Results are given as functions of disorder and aspect ratios of the ring. The
magnitude of the disorder-averaged current may be larger than the
root-mean-square fluctuations of the current from sample to sample even when
the mean free path is smaller, but not too small, than the circumference of the
ring. Then a measurement of the persistent current of a typical sample will be
dominated by the magnitude of the disorder averaged current.
