138 ALTERNATING CURRENTS ' 



the alternator armature. The vector addition is performed by 

 completing the parallelogram having V and IZ for its adjacent 

 sides. The diagonal E' is the vector sum of IZ and V and repre- 

 sents the induced emf . 



The same result is obtained by adding the IR drop directly to F, 

 Fig. 144 (6), and then adding the IX drop, at right angles to / and 

 leading, at the end of IR. The vector addition in this case is 

 made by the use of the triangle of vectors described in Chap. I, 

 page 12. The impedance drop IZ is shown dotted in Fig. 

 144 (6) as it is not used in obtaining E' by this particular 

 method. 



It is to be noted that with a load of unity power-factor the 

 current is in phase with the terminal voltage, but lags the gene- 

 rator induced voltage by an angle oi.v^ 



It is a simple matter to find E' if the other quantities are known. 

 E' is the hypotenuse of a right triangle of which (V -f- IR) is 

 one side and IX the other. 



E' = V(V +IR) 2 +(IX)* (38) 



Example. A 60-kv-a., 220-volt, 60-cycle alternator has an effective arma- 

 ture resistance of 0.016 ohm and an armature reactance of 0.070 ohm. 

 What is its induced emf. when the machine is delivering its rated current 

 at a load power-factor of unity? 



The current / = p = 273 amp. 



IR = 273 X 0.016 = 4.37 volts. 

 IX = 273 X 0.070 = 19.1 volts. 



E' = V(220 + 4.4) 2 + (19.1) 2 = 225 volts. Ans. 



Lagging Current. When the current lags the terminal voltage 

 by the angle 6, the same method is employed to calculate the -in- 

 duced emf. Figure 145 (a) shows the current / lagging the 

 terminal voltage V by the angle 0. The IR drop is along the 

 current vector I, and the IX drop is in quadrature with I and 

 leading, as before. The resulting impedance drop IZ is then 

 found, being the resultant of IR and IX. This impedance drop 

 is then added vectorially to 7, giving the armature induced emf., 

 E'. It will be noted, Figs. 144 and 145, that the position of the 

 armature impedance triangle is determined by the current and 



