Magnetosphere-ionosphere coupling entails the interaction of two quite different plasmas. The magnetosphere is to a large extent a collisionless magnetohydrodynamic (MHD) fluid, while the ionosphere is strongly collisional. As such the relationship between the electric currents and electric field appear to be fundamentally different in the two regimes. For the magnetosphere the currents are determined by the forces within the plasma, while in the ionosphere the current and electric field are related through an anisotropic Ohm's law. Here we explore the transition between these two regimes and show that there is a clear ordering of the governing equations, with a single collisional Ohm's law that contains both the collision-frequency-dependent Pedersen and Hall conductivities and collisionless MHD terms, without making any prior assumptions concerning the ordering of the collision frequencies. The generalized Ohm's law of MHD is also present, but this equation reduces to the statement that within the ionosphere the magnetic field is frozen to the electron fluid, unless electron collision frequencies become comparable to the electron gyrofrequency. It is the freezing-in of the electron fluid that leads to the direct equivalence of mechanical and electromagnetic loads. This equivalence of loads also indicates that Poynting flux traveling upward out of the ionosphere can only occur if there is a convergence of horizontal Poynting flux in excess of the ionospheric Joule dissipation. ¿ 2001 American Geophysical Union