These two models use thin cuts with the H-phi formulation in COMSOL Multiphysics 5.5 to efficiently model transport currents in superconducting materials. The magnetic scalar potential is set to be discontinuous along the thin cuts, thereby imposing a current inside the domain surrounded by the cut equal to the jump in phi. The first model calculates the AC losses in a 2D-axisymmetric pancake coil consisting of 40 turns of superconducting tapes. The second model calculates the AC losses in two twisted superconducting filaments in 3D. A modified periodic condition is introduced to properly consider the periodicity of the field. The equation view must be enabled in order to see the periodic boundary condition used in the phi physics.