An analytical method for computing the instantaneous transient magnetic flux and the eddy currents losses in the armature of an actuator driven by current is proposed. The analytical method consists in modeling the armature by a circuit with reluctances and "eddy inductances". The difference between this work and the previous ones is the fact that the analytical expressions of reluctances and "eddy inductances" are identified from the Joule effect losses and the magnetic energy in the studied armature, when a known sinusoidal magnetic flux goes through it. The presented analytical model takes into account the skin effect and brings a better accuracy on a larger range of frequency. A ladder circuit of fixed value reluctances and "eddy inductances" is also introduced, in order to approximate the response of the "exact" circuit. In that case, it is more practical for time response study and circuit simulations.