228 ALTERNATING CURRENTS 



136. Single -phase Induction Motors. Theory of 

 Motor at Rest 



Induction motors are also used on single-phase circuits. The 

 stator winding in such motors consists of a single-phase winding, 

 while the rotor has a winding of precisely the same type as in 

 polyphase motors. A two-phase induction motor may be run as a 

 single-phase motor by using only one of the phases in the stator 

 winding. 



We shall suppose the single-phase stator winding to be so arranged 

 as to give rise to a sine wave of magnetic induction in the air- 

 gap. The stationary or simple alternating sine wave of induction so 

 produced may be written in the form ( 18) 



b = B sin.pt. sin -x (1) 



where b is the magnetic induction at time t at a point distant x from 

 the origin, the latter being taken at a point where the induction is 

 always zero; T stands for the pole-pitch or half the wave-length 

 ('/ 18). 



FIG. 144. To illustrate Theory of Single-phase Induction Motor. 







In order to simplify the treatment as much as possible, we shall 

 suppose the rotor winding to consist of isolated coils, each short- 

 circuited on itself, the width of a coil being equal to the pole-pitch T. 

 One such coil is shown in Fig. 144, the left-hand side of the coil 

 being at a distance x from the origin. The sine curve shows the dis- 

 tribution of the induction at time t, so that the maximum value of the 



