SYNCHRONOUS MACHINERY 229 



but for a sine wave the ratio of the maximum to the average 

 ordinate is -, and therefore the maximum e.m.f. is 



and the effective value is as before 



E = ^= = 4.44 fn$ 10~ 8 . 



V2 



The e.m.f. generated in an alternator is directly proportional 

 to the frequency /, to the number of turns in series n and to the 

 flux under each pole <. 



In a two-pole machine one revolution or 360 mechanical de- 

 grees corresponds to one cycle or 360 electrical degrees and the 

 frequency is equal to the number of revolutions per second; in a 

 p-pole machine the e.m.f. goes through a complete cycle when 



7? 



the coil moves across a pair of poles and thus through -^ cycles 



2i 



T) 



in one revolution. In this case 360 mechanical degrees = S X 360 



2 



T) 



electrical degrees or one mechanical degree = electrical degrees. 



a 



The frequency in a p-pole alternator revolving at N r.p.s. is 



f = ^N cycles per second ..... (231) 



139. Form Factor. If the flux in the air gap is not so distrib- 

 uted as to give a sine wave of e.m.f., the average value of the 

 generated e.m.f. is still given by equation 230, 



E avg = 4/n$ 10- 8 , 

 but the ratio of maximum to average value is not and the ratio 



of effective to maximum value is not ^ 



V2 



The effective value of the general alternating wave can be ex- 

 pressed as 



E = 4 yfn$ 10~ 8 volts, ..... (232) 



where 7 is called the form factor of the wave and is defined as 

 the ratio of the effective value to the average value of the ordi- 

 nate of the wave. 



