More than 200 hours of Chatanika radar elevation scan data have been used to show that the Pedersen current in the ionosphere is limited to a value that is proportional to the planetary magnetic index Kp. By assuming a simple model for the closure of field-aligned currents in the ionosphere, we argue that this limit is equal to the latitudinally integrated field-aligned current intensity. A least-squares fit to the data gives the limiting current intensity J0 by the following expression: J0 (A/km)=97+71¿Kp. As an extension of this result we use a previously derived relation between polar cap potential drop and Kp to establish a current-voltage relationship for the magnetosphereic generator. We also show how results can be used to put an upper limit on the Joule heating rate for a given polar cap potential drop.