98 ELEMENTS OF ELECTRICAL ENGINEERING. 



the generator is used. In the case of the motor, on the other 

 hand, the speed is determined by these fundamental equations, 

 inasmuch as all the other quantities in these equations are, as a 

 rule, fixed in value by the conditions under which the motor is 

 used. Therefore, the most convenient form of equation (23^:) is 

 that which gives speed in terms of the other quantities. Solving 

 equation (23^) for speed, we have 







Another useful form of this equation is that which expresses 

 I a in terms of the other quantities, namely : 



E - <$>Z' 



From this equation it is evident that the current / o is not in 

 general equal to E x divided by R a , inasmuch as a small part only 

 of E x is used to overcome resistance. When the motor is not 

 running, that is when n = o, then 7 o is equal to E x divided by R at 

 and the value of 7 o is excessively large. To avoid this excessive 

 flow of current when ;/ is small, an auxiliary resistance must be 

 connected in series with the armature as explained in Art. 59. 



Torque. Another equation of considerable importance in the 

 discussion of the motor is the expression for torque. The value 

 of the torque with which the held magnet acts upon the armature, 

 may be derived by considering the side push on each armature 

 wire, multiplying each side push by its lever arm, namely the 

 radius of the armature, and adding these results together. This 

 method of derivation, however, repeats many of the essential con- 

 siderations involved in the derivation of the ftTScfamental equa- 

 tion of the dynamo as given in Art. 30. It is simpler to derive 

 the expression for torque directly from the fundamental equation 

 (23) with the help of Lenz's law as follows : 



The rate at which work is done, in watts, in forcing the cur- 

 rent 7 a through the armature in opposition to the counter elec- 



