Field‐aligned electrons accelerated upward from the ionosphere to the magnetosphere are the principal charge carriers in the auroral downward field‐aligned current region. Current densities, typically of the order of a few μAm−2, are sustained by potential drops of several 100 V up to a few kV. This paper uses a model presented in a separate paper in this special section (Cran‐McGreehin and Wright, 2005) to obtain an analytical nonlinear current‐voltage relationship for the downward current, which is complimentary to the well‐known linear current‐voltage relation for the upward current region (Knight, 1973). Exact and approximate current‐voltage relations are given. These relations are compared with FAST observations and show good agreement.