A new model based on the generalized Lorentzian velocity distribution function (VDF) is used to estimate the total current density Jtot along the magnetic field lines as a function of the field-aligned electric potential difference V between the ionosphere and the magnetosphere. As in the earlier kinetic models based on the Maxwellian VDF, Jtot is a nonlinear function of V, except for values of V between 0.1 and 10 kV, where the current-voltage relationship becomes linear. The effect of an enhanced population of suprathermal particles in the tail of the VDF is to increase the value of the applied potential for which the linear relationship is a valid approximation. The application of this current-voltage relationship to the auroral precipitation region and return current region is discussed. ¿ American Geophysical Union 1996