130 TREATISE ON ALTERNATING CURRENTS. 



which is double the current corresponding to the maximum 

 output. 



The corresponding value of the counter E.M.F. may be shown 

 to be 



e= (8) 



MINIMUM CURRENT AT GIVEN POWER. 



85. Taking the equation 



w + i*r = iE cos if 



and equating , - to zero, we see that, whatever be the output of the 



motor, the current is a minimum (for that output) when if = 0, 

 that is, when the current is in phase with the impressed P.D. 



FUNDAMENTAL EQUATION OF SYNCHRONOUS MOTOR. 



86. With notation as above, p. 127, we have 



w = ie cos 

 and 



& = e* + Pi* - 2eli cos (0 - 0) (From Fig. 42, p. 128.) 

 Also 



a r - D $ 



cos 6 = -j ; sin 6 = -j. 

 therefore 



= 



This equation is called by Steinmetz the " fundamental equa- 

 tion." For a given output and applied P.D. this equation gives 

 the relation between the current and the counter E.M.F. It is, in 

 fact, the equation to the characteristic curve of the machine. 



PLANT CONSISTING OF AN ALTERNATOR AND SYNCHRONOUS 



MOTOR. 



87. The above fundamental equation obviously retains the 

 same form if E represents the E.M.F. of the generator, T the total 

 resistance, and / the total impedance of the two armatures and 



