296 ELEMENTS OF ELECTRICAL ENGINEERING. 



relation between the electromotive force induced in the rotor 

 windings by the pulsation of a flux (4> or 4> c ) and the electro- 

 motive force produced in the rotor windings by the cutting of a 

 flux (3> or 4> c ), as shown in Figs. 255 and 256. Electromotive 

 forces due to pulsation are in time quadrature with the alternating 

 flux, and electromotive forces due to motion are in time phase 

 with the alternating flux ; electromotive forces due to pulsation 

 are greatest in the rotor rods distant 90 from the axis of the 

 flux, whereas electromotive forces due to motion are greatest in 

 the rotor rods which are near the axis of the flux, as shown in 

 Figs. 255 and 256. Furthermore, a certain frequency of pulsa- 

 tion in Fig. 255 gives certain definite values of induced electro- 

 motive force in the rotor rods, the same frequency of rotation in 

 Fig. 256 gives exactly the same values of induced electromotive 

 force in the rotor rods, and a reduced frequency of rotation in Fig. 

 256 gives proportionally reduced values of induced electromotive 

 force in the rotor rods. See Appendix B, Art. 15. 



Generally the rotor is of the squirrel-cage type presenting a 

 multiplicity of independent short-circuits, and it is necessary for 

 the sake of brevity and clearness to devise a scheme whereby one 

 may speak of the electromotive force induced in the rotor, of the 

 rotor current, and of the rotor resistance R", as if the rotor wind- 

 ing were a single circuit with respect to the induced electromotive 

 force or current under consideration. To do this the rotor wind- 

 ing must be reduced to its primary or stator equivalent as follows : 



Let a be the number of conductors in one stator band and 

 let b be the number of rotor rods which for any given position 

 of the rotor lie under the stator band. Then, for a given load 

 current /' in the stator winding, the current in each of the b 

 rotor rods is al' jb, and, if b is an even number, the currents 

 in the successive portions of the short-circuiting end-rings are 

 al 1 \b y 2al \b, $al'lb-- up to \al f , counting from the center 

 of a band (or \al' \b t \aP\b, */'/... up to \al' if b is 

 an odd numb'er). The current throughout the portions u and v, 



