246 ALTERNATING CURRENTS 



as a simple continuous-current generator would be 0'5858VI m . Its 



y i 

 output as a single-phase converter is, however, only 



= 0'5VI m . Thus the single-phase converter output of a continuous- 

 current armature is, for a given average temperature rise, only 



0'5 



or 854 per cent, of its continuous-current output. 



U'OoUo 



145. Heating of Converter having N Slip- rings 



A similar mode of investigation might be applied to a two-phase 

 converter. We shall, however, find it convenient to develop a perfectly 

 general method applicable to any number of slip-rings. Let there be N 

 slip-rings, dividing the armature winding into N phases. The angle 

 ROS (Fig. 152) subtended by each phase at in the case of a two- 



pole armature is -^. If V = continuous voltage between brushes, 



then, by applying the method explained in 141 for determining the 



N 

 slip-ring voltage, we have, putting d = -~, and using formula (1) 



of 141- 



maximum voltage of each phase = V sin ^ 



Hence if I N = maximum current in each phase, then, assuming 

 a power factor of unity, the power supplied to each phase of the 



converter is ^VI N sin , and the total power = number of phases 



N 7T 



X power per phase = -~ VI N sin ^. Let I be the current on the 



i JN 



continuous-current side, so that VI = output on continuous-current 

 side. Neglecting losses in the converter, and equating the input to 



the output, we get -~ VI N sin ^ = VI, or 



I = -^ ........ (2) 



VT ' ** 



N sm,r T 



N 



In Fig. 152, R and S are the points of connection of two neigh- 

 bouring slip-rings, and BiB 2 is the line of brushes, making, at time t, 

 an angle pt 6 with OR. If % = instantaneous alternating current 

 supplied to the phase RS (through the slip-rings at R and S), we 

 may write 



in = I N Sin (0 + a) 



