94 ALTERNATING CURRENTS 



less than the arithmetical one, an increase in the number of slots 

 per pole per phase results in a lowering of the e.m.f. (other things 

 remaining the same). In spite of this disadvantage of a distributed 

 as compared with a uni-slot or concentrated winding, distributed 

 windings are invariably used nowadays, as they tend to reduce 

 armature reaction and give rise to a smoother e.m.f. wave. 



If the shape and size of the pole-shoe are such as to give rise to 

 a distribution of the flux in the gap according to the simple sine law, 

 the value of the e.m.f. in any given case is easily calculated. By way 

 of example, we shall calculate the e.m.f. in one phase of a three-phase 

 generator having six slots per pole, or two slots per pole per phase. 



Let N = flux per pole, n = frequency, and C = conductors per 

 phase. Since each conductor cuts 2N lines per period, the arithmetic 

 mean value of the e.m.f. induced in it is 2Nw (in C.G.S. units). The 

 form factor of a sine wave being I'll ( 3), the r.m.s. value, in volts, 

 of the e.m.f. in each conductor is 



2-22Nw . 10 ~ 8 



The conductors of each phase may be divided into two sets 

 (corresponding to the two slots per pole per phase), such that the 

 e.m.f.'s of all the conductors in one set are in phase with each other. 

 There being C conductors in each set, the r.m.s. value per set is 

 1'llCNfi . 10 ~ 8 . Now, since the distance apart of two neighbouring 

 slots is of the pole-pitch, the phase difference between the e.m.f.'s 

 in the two sets of conductors is . 180, or 30. Hence, compounding 

 the e.m.f.'s of the two sets vectorially, we find for the r.m.s. value of 

 the e.m.f. per phase 



2 . l-llCNn . 10~ 8 . cos 15 = 2'UCNn . 10~ 8 * 



In practice, however, the flux is not distributed according to the 

 simple sine law, but is mainly concentrated under the polar arc, and 

 in accordance with the explanation already given regarding the effect 

 of narrowing the pole-piece, such a concentration of flux results in 

 a higher value of the e.m.f. than that calculated on the assumption 

 of a sine distribution. 



46. General Formula for e.m.f. of Alternator 



The formula for the e.m.f. of each phase of an alternator may be 

 written in the form 



E = 



* The e.m.f. between two machine terminals is, for a star-connected winding, equal 

 to 1'73 times the phase e.m.f. ( 16). 



