The modelling of both critical and remanent states (i.e., the current density and field distributions) in periodic arrays of flat superconducting strips is important for calculating the AC losses in multifilamentary tapes made for power applications. We model the current and field profiles for such magnetically coupled conductors, and have measured these dependences for BSCCO-22223 tapes using a miniature scanning Hall probe technique. The results indicate that the filaments are also electrically connected to a significant extent, which must be caused by superconducting intergrowths between individual filaments.