We consider a mathematical model which describes the frictional contact between an electro-viscoelastic body and a conductive foundation. The contact is modelled with normal compliance and a version of Coulomb's law of dry friction, in which the stiffness and a friction coefficients depend on the electric potential. We derive a variational formulation of the problem and, under a smalness assumption, we prove an existence and uniqueness result. The proof is based on arguments on evolutionary variational inequalities and fixed point. Then, we introduce the fully discretized problem and present numerical simulations in the study of a two-dimensional test problem which describes the process of contact in a microelectromechanical switch.