We show that during magnetospheric substorms there is a clear tendency for the westward electrojet current to follow a characteristic curve that can be matched with an exponential equation. The substorm recovery phase has a characteristic timescale, or exponential time constant, that does not vary substantially from one substorm to the next. There is a slight trend toward shorter substorms as the peak magnitude of the electrojet current increases. This behavior can be explained by a simple model of the coupling between the currents and electric fields in the magnetotail and ionosphere. We derive an equation for the evolution of the substorm currents, including those in the magnetotail, using fundamental physical principles. There is good agreement between the measured and predicted time constants. This model is also consistent with other reported measurements of plasma flows and magnetic perturbations in the magnetotail.