250 ELECTRICAL ENGINEERING 



148. General E.M.F. Equation. The electromotive force equa- 

 tion, derived in Art. 139, 



E = 4 yfn$ 10- 8 volts 



which applies only to concentrated windings may be extended to 

 include all windings by introducing the distribution factor 5. 



Thus the general equation for the effective value of the e.m.f. 

 between terminals of an alternator is 



E = 4 8yfr& 10- 8 volts, ..... (244) 

 where 



/ = frequency in cycles per second, 



n = number of turns in series between terminals, 



3> = flux from one pole, 



7 = form factor of the e.m.f. wave, 



5 = distribution factor of the winding. 



This equation holds both for the single-pha.se alternator and for 



any phase of a polyphase alternator with n turns in series per phase. 



If the winding is short pitch the e.m.f. is reduced in the ratio 



cos : 1 where the coil pitch is 180 a electrical degrees. 



2 



149. Rating of Alternators. Alternators are designed to give 

 a certain terminal voltage and to supply any current up to a 

 certain maximum or full-load current. 



The output is 



P = nEI cos 6 watts, 

 where 



E is the voltage per phase, 



I is the full-load current per phase, 



cos 6 is the power factor of the load, and 



n is the number of phases. 



The power output, therefore, depends on the voltage which is a 

 fixed quantity, the current which is variable and is limited by the 

 allowable temperature rise caused by the copper losses and other 

 losses in the machine, and the power factor of the load over which 

 the designer has no control. 



Alternators should, therefore, be rated not in watts or kilowatts 

 which depend on the power factor but in volt amperes or kilovolt 

 amperes. 



A machine rated at 1000-kilovolt amperes can supply 1000 kilo- 



