In this paper we use a three-dimensional magnetohydrodynamic (MHD) model to study the response of the magnetosphere-ionosphere system to a sudden change in the sign of the By component of the interplanetary magnetic field. We find that after such a change the magnetosphere responds as a linear system and the ionospheric potential can be very accurately represented by a linear superposition of the initial and final distributions of the ionospheric potential. Although heuristic in nature, this representation of ionospheric potentials significantly simplifies the analysis of the time-dependent output of the model. The accuracy of this decomposition of the ionospheric potential is discussed. This decomposition also helps to define, in a very intuitively clear way, the bow shock to ionosphere communication time and the ionospheric reconfiguration time. We find that in our model simulation the reconfiguration time depends on the strength of the interplanetary magnetic field (IMF) and the solar wind speed but not on the ionospheric conductivities. The communication time in our model has a typical value of 300--400 s and the reconfiguration time is approximately 300--450 s. These characteristic times are generally consistent with observations and earlier modeling results.