(HAP. IV] INDUCED E.M.F. . 79 



the air-gap can be varied within wide limits, and consequently 

 that component of the field which is sinusoidal can be varied. The 

 result is that the ratio of the direct to the alternating voltage is 

 also variable. Namely, we have seen before that the value of the 

 continuous voltage does not depend upon the distribution of the 

 flux, but only upon its total value, while the effective value of the 

 alternating voltage depends upon the sine wave or fundamental 

 component of the flux distribution. 1 



Prob. 42. Check some of the values given in the table above. 



Prob. 43. A three-phase rotary converter must deliver direct current 

 at 550 v. What is the voltage on the alternating-current side? 



Ans. 337 v. 



Prob. 44. The same rotary is to be tapped in three additional places so 

 as to get two-phase current also. How many different voltages are on 

 the alternating-current side and what are they? 



Ans. 389,337,275,195,100. 



Prob. 46. The table given above holds true only when the flux density 

 is distributed approximately according to the sine law. Show how to 

 determine the ratio of alternating to continuous voltage in the case of two 

 collector rings connected to taps 180 electrical degrees apart, when the 

 curve of field distribution is given graphically. Solution : Divide the pole 

 pitch into a sufficient number of equal parts and mark them on a strip of 

 . Place the strip along the axis of abscissae. The sum of the ordi- 

 nates of the flux-density curve, corresponding to the points of division, at 

 a certain position of the strip, gives the instantaneous value of the alter- 

 nating voltage. Having performed the summation for a sufficient number 

 of positions of the strip, the wave of the induced e.m.f. is plotted. The 

 scale of the curve is determined by the condition that the maximum ordi- 

 nate is equal to the value of the continuous voltage. The effective value is 

 found in the well-known way, either in rectangular or in polar coordinates 

 (see the Electric Circuit). 



Prob. 46. Apply the solution of the preceding problem to the field dis- 

 tribution specified in Prob. 30, Art. 30. Ans. 81.5 per cent. 



Prob. 47. Extend the method described in Prob. 45 to the case when 

 tin- Distance between the taps connected to the slip rings is less than 

 180 degrees. Show how to find the scale of voltage. 



Prob. 48. How does a fractional pitch affect the values given in the 

 table above, and the solution outlined in Prob. 45? 



Prob. 49. Show how to solve problems 15 to is \\hcn the field curve 

 is given analytically, as B /**(), for instance in the form of a Fourier 

 series. Hint : See C. A. Adams " Voltage Katio in Synchronous Conver- 

 ters with Special Reference to the Split-pole Converter,' 1 Trans. Amer. 

 Wee. Engs., Vol. 27 (1908), part 1 1. p. 959. 



l SeeC. W. Stone, "Some DevHopm. -UN in Synchronous Convertere," 

 Tram. Amer. Inst. Elec. Bngn., Vol. 27 (1908), p. 181. 



