An experimental and numerical study of electrical contact for low currents in sphere-plane set-up is presented. A three-level multi-scale model is proposed. We use the finite element analysis for macroscopic mechanical and electric simulations. It takes into account the setup geometry, elasto-plastic mechanical behavior of contacting components in the finite-strain-plasticity framework and electrostatic properties. A sensitivity analysis with respect to the brass plastic behavior and to the thickness of coating layers is also performed. The finite element results are used for an asperity-based model, which includes elasto-plastic deformation of asperities and their mutual elastic interactions. This model enables us to simulate the real morphology of contact spots at the roughness scale using the experimentally measured surface topography. Finally, the Greenwood multi-spot model is used to estimate the electrical contact resistance. This three-level model yields results which are in good agreement with experimental measurements carried out in this study.