In this paper numerical simulations are presented of the reversed field pinch (RFP) dynamo effect utilizing the resistive magnetohydrodynamic (MHD) equations in the quasilinear approximation. In addition, a mean field equilibrium magnetic field configuration is constructed in cylindrical geometry by dropping inertia on the symmetric radial component of the velocity field. Results are obtained for a variety of operating conditions: flat‐top current, current ramp‐up, and ramp‐down. It is found that the Alfve´n time, although present in the equations describing the perturbed quantities, is not important on the long resistive run time; the result is a three‐dimensional Ohmic equilibrium with symmetric mean toroidal magnetic field reversal. Using these results, and in view of recent RFP experimental data, a simple correspondence between global MHD behavior in the RFP and the tokamak is given.