176 



TREATISE ON ALTERNATING CURRENTS. 



In order to make our calculation clear and intelligible, con- 

 sider the case in which the armature is star-wound as in Fig. 75, 

 and let a\ y a% be two diametrically opposite coils, connected at N, S, 

 to two diametrically opposite commutator segments. 



It is obvious that if E is the voltage between the commutator 



brushes, then E is equal to the maxi- 

 mum value of the sum of the alter- 

 nating E.M.F.s generated in a\ and 

 ct% conjointly ; that is, is twice the 

 maximum value of the alternating 

 E.M.F. in ai alone. It is also 

 obvious that if all the coils are 

 electrically connected at 0, the result 

 will be the same as if they were not 

 connected there. is called the 

 neutral point. 



We thus see that the maximum 

 value of the E.M.F. generated be- 

 tween the free end of the coil a\ 



(Fig. 75) and the neutral point is half the E.M.F. between the 

 commutator brushes. 



Also the E.M.S. value of the E.M.F. is ^ times the maximum 



value ; therefore if E\ is the E.M.S. value of the E.M.F. generated 

 between the free end of the coil a\ and the neutral point, \ve 

 have 



Now revert to the mesh- winding shown in Fig. 76, and let a\, 0%, a 3 

 be successive tappings connected to adjacent collector-rings, and 

 let the vectors OEi, OE^ etc. (Fig. 77), represent the E.M.S. values 

 of the E.M.F.s between a\, a%, etc., and the (in this case fictitious) 

 neutral point ; then the vector E\ J% represents the E.M.F. be- 

 tween two adjacent collector-rings. But the angle E\OE% = ; 

 therefore 



EA - 2 . OE l sin - 



n 



= 7= sin (4) 



\/2 n 



