CHAP. IV] INDUCED E.M.F. 65 



ive and the average values of the voltages is equal to 

 or 1.1 1. 1 If the shape of the induced e.m.f. departs widely from the 

 sine wave the actual curve must be plotted and its form factor 

 determined by one of the known methods (see the Electric Cir- 

 cuit). Let the form factor in general be and let the machine 

 have N armature turns in series per phase, or what is the same, 

 2N conductors in series. The total induced e.m.f. in effective 

 volts is then 



(30) 



This formula presupposes that there is but one slot per pole per 

 phase, so that the e.m.f s. induced in the separate conductors are all 

 in phase with each other, and that their values are simply added 

 together. In reality, there is usually more than one slot per pole 

 per phase, for practical reasons discussed in the next article. It 

 will be seen from the figure that the e.m.fs. induced in adjacent 

 slots are somewhat out of phase with each other, because the crest 

 of the flux reaches different slots at different times. Therefore, 

 the resultant voltage of the machine is somewhat smaller than that 

 according to the preceding formula. The influence of the dis- 

 tribution of the winding in the slots is taken into account by mul- 

 tiplying the value of E in the preceding formula by a coefficient k tl . 

 which is smaller than unity and which is called the breadth factor. 

 Introducing this factor, and assuming =1.11, which is accurate 

 enough for good commercial alternators, we obtain 



(31) 



where 9 is now in megalines. Values of k b are given in t he art ides 

 that follow. 



Formula (31) applies equally well to the polyphase induction 



runt r or generator. There we also have a uniformly revolving 



flux in the air-gap, the flux density ban- distributed in space, 



Ming to the sine law. This gliding flux induces e.m.fs. in the 



r and rotor windings. The only difference between th< 



kinds of machines is that in the synchronous alternator the field is 



made to revolve by mechanical means, while in an induction 



machine the field is excited by the polyphase currents flowing in 



tin proportion* of A pota-flhoo which very nearly give * due wave 

 see Arnold, Werhstbtromttchnik, Vol. 3, p. 247. 



