308 ALTERNATING CURRENTS 



conductor a is opposite the center of a pole. It is zero when the 

 pole reaches such a position that conductor a lies midway be- 

 tween the poles. The value of this emf ., e, for any position of the 

 pole axis Y-Y, is shown by curve e. 



Assume that a load is now applied to the motor shaft. This 

 must result in momentary slowing down of the rotor, since it 

 requires time for a motor to take increased power from the line. 

 Therefore, the rotor instead of being in the position shown by the 

 solid lines in Fig. 285 (a) will occupy a given position in space 

 at a later time on account of the effect of the load torque. The 

 relations under this condition are shown by the dotted lines. 

 Because of the application of load, the pole center is now at Y'Y' 

 instead of being at YY. Therefore, the induced emf. will not 

 reach its maximum value at the same instant that it would have 

 reached it had no load been applied. This maximum value 

 now occurs later in time, due to the slight backward angular 

 displacement of the rotor. This is shown by a new curve of 

 induced emf;, e', lagging e by an angle a where e is the emf. which 

 would have been induced had no load been applied to the rotor 

 shaft. 



This is further illustrated by the use of vectors. Assume that 

 the motor is running without load and that the current is so 

 small that the back emf., E, Fig. 285 (6), is sensibly equal to 

 the terminal voltage V and is 180 out of phase with V. (E is 

 the component of the terminal voltage necessary to balance 

 the back emf., E). The vector sum of V and E is zero, 

 practically. 



Now apply load. The terminal voltage V is assumed to be 

 constant and so is not affected by the load. The induced or 

 back emf., E, will be shifted backward by an angle a because 

 of the backward angular displacement of the rotor caused by 

 the load. Let this new value of back emf. be E' and let the 

 component of terminal voltage necessary to balance it be E'. 

 The vector sum of V and E' is no longer zero. Therefore, a 

 vector difference exists between V and E'. 



In the direct-current motor, the armature current is given by 

 dividing the armature resistance into the difference between the 

 terminal voltage and that component of the terminal voltage E 

 which balances the back emf. E. In the synchronous motor, 



