We study the stationary state of Hall devices composed of a load circuit connected to the lateral edges of a Hall bar. We follow the approach developed in a previous work [Creff et al., J. Appl. Phys. 128, 054501 (2020)] in which the stationary state of an ideal Hall bar is defined by the minimum power dissipation principle. The presence of both the lateral circuit and the magnetic field induces the injection of a current: the so-called Hall current. Analytical expressions for the longitudinal and transverse currents are derived. It is shown that the efficiency of the power injection into the lateral circuit is quadratic in the Hall angle and obeys to the maximum transfer theorem. For usual values of the Hall angle, the main contribution of this power injection provides from the longitudinal current flowing along the edges instead of the transverse current crossing the Hall bar.