62 A Theory of the Synchronous Motor. 



That the equation is satisfied by (a) is obvious, and we see 

 that it is satisfied by the points (b) and (c) by writing it in 

 the form / E \ 2 £> E 2 



V 2R/ + R == 4B2* 



7. Thus we see that the curve of minimum current at given 

 power passes through the points of 



(a) zero current and zero power ; 



(b) maximum power ; 



(c) maximum current and zero power. 



E 



We notice that the maximum current at no load is c = s , 



sx 



E 



whereas if the motor were at rest the current would be c= y; 



that is, the maximum current at no load is in all cases greater 

 than the maximum current if the armature is at rest. 



8. Again, from the equation 



jt9 + uV = cE cos yjr 



we have . . p 4- cV 



* = cos ^E~' 



therefore d^fr _ c 2 r —p 



~dc~~ cs/ {c*W-(p + cV) 2 } 

 = 

 when p = cV. 



^ is then a maximum, and we see that the maximum differ- 

 ence of phase between the current and the impressed E.M.F. 

 takes place when the electrical efficiency is ^. 



9. Example. — Suppose we have a 50 kilowatt motor driven 



by a 1000 volt generator, and suppose that R = 3 ohms and 



S = 4 ohms, so that 1 = 5 ohms. 



10 6 

 Then maximum output . . = — - = 83*3 kilowatts. 



Corresponding current . . =—^-~ = 166*7 amperes. 



„ counter E.M.F. =^2.= 833*3 volts. 



b 



Maximum current running light = — x— = 333*3 amperes. 



o 



Corresponding counter E.M.F. =— ^ — = 1333*3 volts. 



o 



&C. 



