Work is reported on development and analysis of a model for quantum rings in which persistent currents are induced by Aharonov-Bohm or other similar effects. The model is based on a centric and annual potential profile. The time-independent Schrodinger equation including an external magnetic field and an Aharonov-Bohm flux is analytically solved. The outputs, namely energy dispersion and wave functions, are analyzed in details. It is shown that the rotation quantum number is limited to small numbers, especially in weak confinement, and a conceptual proposal is put forward for acquiring the flux and eventually estimating the persistent currents in a Zeeman spectroscopy. The wave functions and electron distributions are numerically studied and compared to 1D quantum well. It is predicated that the model and its solutions, eigen energy structure and analytic wave functions, would be a powerful tool for studying various electric and optical properties of quantum rings