ALTERNATING CURRENTS 



find its direction at the time t, we notice that if 6 be the angle which 

 it makes with the vertical axis 



/yi 



tan 9 = - = tan pt 



y 



so that 



Om ft 



The angle therefore changes at a constant rate, i.e. the field 

 rotates with the constant angular velocity p. 



XTYjU 



a 



UUULiJ 



FIG. 22. Production of Rotating Field by 

 Two-phase Currents. 



n 



FIG. 23. Rotating Field produced by 

 Three-phase Currents. 



Consider next three coils, I, II, and III, arranged at 120 to each 

 other, as shown in Fig. 23, and conveying the three currents of equal 

 amplitude 



i\ = I sin pt 



iz = I sin (pt + ~J = - 1 sin pt + -^- 1 cos pt 



= sn 





cos 



The directions of the magnetic fields produced by the three coils 

 at their common centre are indicated by x, u, and v in Fig. 23. The 

 values of these magnetic fields are given by 



x = M sin pt 



sin pt + X>-M cos Pt 



LI 



v = - 



w 



sin pt ~-M cos pt 



