28 ELECTROMOTIVE FORCE AND CURRENT. 



In order to determine from the readings taken the angle 

 of phase difference between the machines, construct for each 

 set of readings a triangle of which the sides represent to 

 some convenient scale the three voltmeter readings. In 

 doing this it will be convenient to draw a horizontal line repre- 

 senting to scale the resultant voltage. From one end of this 

 line draw a circle whose radius is equal on the same scale 

 to the voltage of one alternator. From the other end draw 

 a circle with a radius equal to the voltage of the other 

 alternator. Join the intersection of these circles to the ends 

 of the horizontal line. The triangle so obtained shows 

 graphically the relations between the voltages of the two 

 machines, and the voltage which would be. supplied to a 

 circuit connected to the machines in series. The angle between 

 the inclined sides is the angle of phase difference between the 

 machines. A curve should be plotted showing the resultant 

 voltage at various angles of the coupling. 



The resultant voltage will vary between a maximum when 

 the voltage of both machines is added, and a minimum when 

 the machines are in opposition, when the resultant voltage 

 is the difference between the two. When working in parallel, 

 alternators are excited, so as to give the same voltage, and 

 since they are connected together like terminals to likei 

 the resultant voltage in a circuit connected to the terminals 

 of any one machine is then equal to that of any other 

 machine. Under these conditions a voltmeter connected 

 between the machines at no load in the manner of V z in the 

 diagram Fig. 11, would read zero. 



In carrying out the experiment just described, in order 

 to determine the angle between the machines, it will be 

 found convenient to excite the alternators to give equal 

 voltages. 



As an illustration of this experiment, the curve shown in 

 Fig. 12 has been drawn. Two similar alternators with an 

 adjustable coupling were excited to give 72 volts each. From 

 the graduation of the coupling the resultant value of the 

 voltage was calculated for a series of relative positions of 

 the machines. These values are shown on the curve together 

 with a set of observed values read direct on a voltmeter in 

 series with the machines.* 



!* The resultant value was calculated as follows : 

 EI = E-t = 72 volts = voltage of each alternator. 

 ei = E sin e 2 == E sin (6 + 9) 



