78 THE MAGNETIC CIRCUIT [ART. 32 



direct -current brushes. The same ratio holds true for a two- 

 phase rotary', for the voltages induced in each phase. 



Let now two slip rings be connected at two points of the arma- 

 ture winding, a electrical degrees apart. In order to obtain the 



value of the alternating 

 voltage the vectors of the 

 voltages induced in the 

 individual coils must be 

 added geometrically, as in 

 Fig. 18. With a large num- 

 ber of coils the chords can be 



replaced by the arc, and in 

 FIG. 21. Relation between the alternating \ * 



voltages in a rotary converter. tms wa Y Fl S- 21 1S obtained. 



The diameter MN = ei of the 



semicircle represents the vector of the alternating voltage when 

 the points of connection to the slip rings are displaced by 180 

 electrical degrees, while the chord MP=e a gives the voltage 

 between two slip rings when the taps are distant by a electrical 

 degrees. It will thus be seen that 



e a = ei sin Ja (39) 



But we have seen before that ei=Q.7Q7E, where E is the voltage 

 on the direct-current side of the machine. Hence, for sinusoidal 

 voltages, 



e a = 0.707 Esm^a (40) 



The following table has been calculated, using this formula. 



Number of slip rings 2 3 4 5 6 



Angle between the adjacent taps in electrical 



degrees 180 120 90 72 60 



Ratio of alternating to continuous voltage, in 



percent 70.7 61.2 50 41.5 35.3 



The foregoing theory shows that the ratio of the continuous to 

 the alternating voltage is fixed in a given converter, and in order 

 to raise the value of the direct voltage it is necessary to raise the 

 applied alternating voltage. This is done in practice either by 

 means of various voltage regulators separate from the converter, 

 or by means of a booster built as a part of the converter. Another 

 method of varying the voltage is by using the so-called split-pole 

 converter. In this machine the distribution of the flux density in 



