356 THE INDUCTION MOTOR. 



voltage induced by the rotation, and R = resistance 

 of armature. In this case of the D.C. motor 



e = N v Z when measured in absolute units, and 

 E = N v l Z when v l is the speed of the motor arma- 

 ture, when running without overcoming any resistance 

 to its motion, i.e., at its critical speed or without slip. 



Thus E -e = NZ (v l -v), 



and the current may be said to be proportional to the 

 " slip " of the armature, i.e., to the difference between 

 the actual and the critical speeds. 



In the second place, the torque of a direct-current 

 motor is directly proportional to the product of total 

 field strength and armature current. For a direct- 

 current machine the torque may be written in absolute 

 units 



Z N C 

 T = ^ - when C is the total armature current. 



2i 7T 



If we write, as in the case of the induction motor, c as 

 the current flowing in each conductor, we have 



A 7T 7T 



Since, then, for a parallel-connected armature 



C 



C Ck 



2p 



Thus we can compare the expressions for the torque 

 in the two cases by writing 



Z c N f> 

 T A = - - for direct-current motors. 



7T 



T a = Tjyfr for alternating-current motors. 



A V & 



Also in the case of the direct-current machine, the 

 armature efficiency is inversely proportional to the slip. 

 For the direct-current motor 



C E = C e + C- R, 



but C E is the power supplied to the motor and C 2 R is the 

 power lost in heating the armature conductors, and C e con- 

 sequently represents the useful power exerted by the motor, 



