CHAP. IV] 



INDUCED E.M.F. 



75 



series between the brushes. Each e.m.f. represents an instanta- 

 neous value of an alternating e.m.f.; the e.m.fs. induced in different 

 coils differing in phase from one another, because they occupy 

 different positions with respect to the poles. The voltages induced 

 in the extreme coils of an armature circuit differ from one another 

 by one-half of a cycle. 



Instead of adding the actual instantaneous voltages, it is suffi- 

 cient to calculate the average voltage per coil, and to multiply it 

 by the number of coils in series, because the wave form of the 

 e.m.fs. induced in all the coils is the same, and their phase differ- 



FIG. 20. The cross-section of a direct-current machine. 



ence is distributed uniformly over one-half of a cycle. According 

 to eq. (26) the average voltage per turn per half a cycle is 20/i7\ 

 where \T is the time during which the coil moves by one pole 

 pitch, and is the flux per pole, in webers. Sul>stituting I// for 

 7'. the average voltage per turn is equal to 4/0. Ixt tl 

 turns in scries between the brushes of opposite polarity ; then the 

 induced voltage of the machine is 



I 



(37) 



where 0is now in mepalinps. Thus, in a direct -current machine 

 the induced voltage bet\vr<-n the brushes depmd- mly upon the 

 total useful flux per pole, and not upon its distribution in the air- 



