A theory of magnetosphere-ionosphere coupling in the presence of field-aligned potential drops is formulated within the framework of magnetohydrodynamic equations. Our formulation allows the magnetosphere as well as the ionosphere to respond self-consistently to the parallel potential drop along auroral field lines. Equipotential contours are distorted into a V-shaped structure near the convection reversal boundary and S-shaped on the equatorward side, each gives rise to an inverted V precipitation band. The loading effect of the imperfect coupling results in a valley in the electric field profile which occurs equatorward of the convection reversal boundary.