THE INDUCTION MOTOR. 



353 



The power spent in driving the armature measured 

 in mechanical units = 2 TT n T, where n is the speed 

 of rotation and T is the torque applied. 



The electrical power to which this is equivalent = 

 power output of the dynamo = C- R where C is the 

 current of the armature, and R is the total resistance 

 of the armature and external circuit. Thus we may 

 write 



2-KnT = C 2 R. 



In this equation we may suppose only absolute C.G.S. 

 units to be employed, so as to avoid multiplying by 

 constants. 



In the case of the induction motor a similar condition 

 exists. If each conductor has induced in it a current c, 

 and if there are in all N conductors on the rotor, each 

 with a resistance r, in the short-circuited armature, 

 the total power developed due to the relative rotation 

 of the field and armature will be N c*r. This power 

 must be the equivalent of the mechanical power exerted 

 by the rotating field upon the armature as in the case 

 of the direct-current armature just discussed. Con- 

 sequently, in this case also we may write 



2TrnT = Nc*r (1) 



Where n is the relative speed of the rotating field and 

 the rotor, i.e., the slip, and T is the torque exerted upon 

 the rotor by the field of the stator. 



In the case of the rotor conductors, however, the 

 currents are not constant, but are alternating currents 

 varying according to the E.M.F. induced by the rotating 

 field. 



In order to determine the value of these currents 

 consider Fig. 176, in which the circle represents the 

 circumference of the rotor, and the line X indicates 



FIG. 176. 



