A volume integral formulation to compute eddy currents in non-magnetic conductive media is presented. The current distribution is approximated with facet finite elements. The formulation is general and leads to an equivalent lumped elements circuit. In order to ensure the solenoidality of the current distribution, an algorithm detecting the independent loops is then used for the resolution. The formulation is tested on TEAM workshop Problem 7. Even with coarse meshes, its accuracy is demonstrated.