56 SYNCHRONOUS MOTORS 



F on the power-circle G G f , situated on the phase-line AN. As soon 

 as the point AZ is displaced on the circle to either side of the line AN, 

 the current increases. There is therefore a value of the internal E.M.F. 

 2 which corresponds to a minimum current, and all values greater 

 or less than this value necessitate a stronger current. 



It is evident from Fig. 27, without any explanation, that the minimum 

 value is that which brings the current into phase-coincidence with the 

 E.M.F. EI, i.e., with the E.M.F. at the terminals, since the motor is 

 supposed to be supplied from a constant potential source having neg- 

 ligible impedance. 



[This condition gives, immediately, for the corresponding alge- 

 braical value of E% the following 



2 E 1 RI ........... (25) 



Suppose, for example, a 40 k.w. motor connected to a 2ooo-volt 

 circuit, its efficiency being 77 = 0.85, and the constants being R= 2 ohmSj 

 and =40 ohms. The minimum current necessary, at full load, will 

 be about 



40,000 



/= 5 ; =23.5 amperes; 

 0.85X2000 



whence Z/= 940 volts. 



The corresponding E.M.F. will be 



2= V(2ooo) 2 +(94o) 2 2000X47X2=2166 volts. 



The corresponding value of the exciting current will be obtained by 



reference to the excitation-curve of the alternator. 



V-Curves. The foregoing conclusions, which had already been 



formulated by the author in a paper in 1892 (La Lumiere Electrique, 

 Vol. XLV, pp. 423 and 563), were confirmed 

 experimentally by Mordey in 1893. Mor- 

 dey's results were represented graphically 

 by a curve, in rectangular co-ordinates, to 

 which the name of V-curve has been given, 

 owing to its characteristic appearance (Fig. 

 30). This curve is obtained by taking as 

 FIG. 30. abscissae the values of the E.M.F. E 2 and as 



ordinates the corresponding current-values. 



It is readily seen that the current does pass through a minimum Mm 



for a certain value Om of the voltage. 



