A model for arcs in the cathode region in the presence of a slag layer is given. The are has been assumed to be comprised of two sections; one in the slag layer and the other in the plasma boundary layer. A model for the are consisting of an are column, a spreading region and a diffuse region has been considered. The dimensions of the are, such as are height and diameter, have been obtained. The boundary layer voltage drop, comprised of the are column voltage drop, spreading region voltage drop and diffuse region drop, and the are current have also been obtained.