On calculating losses in current carrying conductors in an external alternating magnetic field

A common approach in calculating ac resistance is to add together losses due to a magnetically isolated conductor and the losses due to eddy currents induced in the same conductor by an externally excited magnetic field in the absence of primary conductor current. This method is employed in the design of large current carrying devices such as multiphase cables and reactive elements. The present analysis shows that this "superposition" method for calculating ac resistance is an approximation which is valid only under restrictive conditions. This is illustrated by calculating the total joulean losses in a single layer coil in Cartesian coordinates and identifying the contributions due to the primary coil current and eddy currents induced by the external field.