304 ELEMENTS OF ELECTRICAL ENGINEERING. 



to overcome the reactance and resistance of the armature wind- 

 ing are XJ and RJ as shown. 



The effect of the current / in flowing through the field wind- 

 ing is to produce an alternating flux <l> through the armature. 

 This flux is in phase with the current and it induces in the arma- 

 ture windings an electromotive force E c which is equal to QZ'n, 

 where <I> is the flux entering the armature from one field pole, 

 Z' is equal to pZlp' -r- io 8 , and n is the speed of the armature 

 in revolutions per second ; / is the number of field poles, Z is 

 the total number of armature conductors, and p 1 is the number 

 of current paths between positive and negative brushes.* Since 

 3> is an alternating flux which is in phase with the field current 

 7, it is evident that E e (equals QZ'ri) is an alternating electro- 

 motive force of the same frequency and in phase with /. There- 

 fore since E c is a counter electromotive force, the portion of the 

 supply voltage which overcomes it is equal to it and is represented 

 by the line E c in Fig. 260, and the total supply voltage is rep- 

 resented by the line OE which is equal to the vector sum of F, 

 A, and E c . 



The power lost in the field winding is R f P, the power lost in 

 the armature is R a l 2 , and the power which is used to force the 

 current against the counter electromotive force E c , namely, E e l t 

 appears as mechanical power. Eddy current and hysteresis 

 losses are ignored in Fig. 260. 



Design of single-phase series motor to give large power factor. 

 It is evident from Fig. 260 that a large power factor (small value 

 of the angle 0) depends upon a large value of E c in comparison 

 with XJ and XJ\ of course R f l and R a l should both be as small 

 as possible because they represent energy losses in the windings. 



(a) In the first place the reactance X a of the armature wind- 

 ing may be reduced nearly to zero by the use of the neutralizing 

 winding as explained in the following article. A neutralizing 

 winding is therefore an important feature of the single-phase 

 series motor. 



* See page 43 of the first volume of this text. 



