Heat losses in the conductors1 of alternating-current machines

WITH the increase in the capacity of alternating-current generators, it has become more and more important to determine the exact relation between the heat developed in any conductor and the currents that it and other neighboring conductors carry. Solutions for the distribution of alternating current within conductors that are embedded in open rectangular slots have been obtained for a number of cases. The methods of attack and the results obtained have heretofore involved trigonometric and hyperbolic functions of real angles. For this reason the work has been unnecessarily complicated, and its scope considerably cramped. Had the investigators used hyperbolic functions of complex angles, they would have accomplished more with much less effort. These hyperbolic functions of complex angles are such a powerful tool in the solution of this current distribution problem that the author feels fully justified in presenting this discussion of their application, even though many of the results have been obtained before.