220 ALTERNATING CURRENTS 



so that there will be a sine wave of e.rn.f. travelling along the rotor 

 conductors, and this sine wave of e.m.f. will give rise to a sine wave 

 of current. Now, if the rotor current were exactly in phase with the 

 hypothetical rotor e.m.f., a simple application of the rule for finding 

 the direction of an induced current would show that the field due to 

 the rotor currents would be as shown by the arrows drawn at intervals 

 along the surface of the rotor core in diagram (a). (This would be 

 approximately the case for very small values of the slip, when the 

 frequency of the rotor currents is so low that they lag by a relatively 

 small amount behind the hypothetical e.m.f. producing them.) Owing, 

 however, to the lag of the rotor currents behind their e.m.f.'s, the 

 hypothetical field due to the rotor currents will be as shown in 

 diagram (c), where the current is supposed to lag by an angle a 

 behind the e.m.f. Similar reasoning will show that if the motor be 



< # H t* it x 



IDEAL CASE : SPEED BELOW SYNCHRONISM. I DEAL CASE ; 3 PE D A 80VE SYNCHKONISM. 



(a) (6) 



-(f*)>! * ?+(?)*. 



' 



SPEED BELOW SYNCHRONISM. SPEED ABOVE SYNCHRONISM. 



(0 V) 



Fia. 140. To illustrate Phase Eelation of Stator and Rotor Currents in Induction 

 Motor and Generator. 



driven above the speed of synchronism, so as to have a negative dip, 

 in which case the sine wave of the stator flux is reversed in its 

 motion relatively to the conductors, the distribution of the hypo- 

 thetical rotor field in the ideal case of no lag is as in (J), while the 

 actual distribution is as in (d). The amount of lag, it is to be noted, 

 depends solely on the slip,* and will have the same numerical value 

 a whether the slip be positive or negative, provided the numerical 

 value of the slip is the same. 



On comparing diagrams (c) and (d), we notice that in passing 

 from any positive value of the slip to an equal negative value, we 

 change the phase difference between the wave of hypothetical rotor 

 flux and that of hypothetical stator flux by an amount TT + 2a. 



* Which determines the frequency of the rotor currents, and hence the angle 

 of lag. 



