Persistent currents are those, which, as its name states, do not change in time. It is a quantum effect revealed in microscopic and mesoscopic systems, in which a charged particle moves around a close geometry, such as a ring, in the presence of a magnetic flux. Specifically. This current is produced for any ring configuration, since the ground state for the electron in the ring is always nonzero. This is due to the shift produced by a phase introduced as a consequence of the magnetic flux, an Aharanov-Bohn phase. The calculation of the persistent current in a ring with several electrons can be reduced from the calculation of the current associated with the energy of an electron, summing over these currents. The simplest model is a metal ring, and a current generated by a single electron.