The use of the scalar product of vectors in locus diagrams of electrical machinery

MOST engineers interested in alternating-current apparatus are familiar with the usual representation of currents and voltages by means of vectors. Such vector diagrams are in common use in the treatment of transmission lines, transformers, alternators, etc. When the performance of a machine, say of an induction motor, varies, due to a changing load, the end of the current vector describes a curve. When this curve can be predetermined, and especially when it is a circle, the study of the performance of that particular machine is much simplified and the electrical relationships are readily visualized. Such locus diagrams are used to a considerable extent for the induction motor and for certain types of alternating-current commutator motors.