The electrodynamic structure of auroral currents is studied in the steady state by coupling Maxwell's equations with effective Ohm's laws for ionospheric Pedersen currents, field-aligned currents and currents in the generator region. An effective generator conductivity is introduced which allows consideration of a variety of states from pure current (&Sgr;G =0) to pure voltage (&Sgr;G →∞) generators. On short time scales when Alfv¿n waves are important, this conductivity mapped to the ionosphere is lower than the ionospheric conductivity implying a currentlike generator. This is in contrast with previous electrodynamic models of the aurora, which have assumed voltage-fixed generators. Current generators differ from the voltage generators in that the natural scale size is smaller for current generators, indicating that the narrow discrete arcs may be current driven, while the overall large-scale auroral currents are voltage driven. In addition, reversals of the electric field occur naturally in the current-driven case, leading to V-shaped potential structures. Examination of the effects of ionospheric conductivity gradients and comparison with a time-dependent MHD model of auroral currents indicate that either regions of nonlinear resistivity or generator motions can decouple the ionospheric currents from the generator. In this case the effective conductivity becomes the Alfv¿n wave conductivity, which, being small compared to the ionospheric conductivity, leads to a structure typical of a current-driven system. This implies that the current structure is not affected by ionospheric conductivity gradients, while the ionospheric electric field is enhanced on the low-conductivity side.