HEATING OF CONVERTER 247 



where the angle o is as yet unknown. In order to determine a, we 

 notice that the phase voltage and current reach their maxima values 

 when T, the middle point of RS, is in line with the middle of the 

 pole-piece, i.e. when the line of brushes is at right angles (as shown 



FIG. 152. To illustrate Heating of Converter with N Slip-rings. 



by dotted line) to OT. We must then have i y = I N , or sin 

 (8 + a) = 1, i.e. 6 -f a = ~ ; but since, referring to the figure, we 



Ll 



at this instant have = ^ -f ^, it follows that a = ^.. We thus 



JN 2i JN 



have 



i y = I N sin (0 - ~) 



Consider now any portion of the winding between R and S, such 

 as that at P, and let ROP = <j>. Then, so long as < $, the current 

 at P is given by 



IH + JI = JI + I N sin O - 

 while for > $ the current at P is 



i* - J I = - U + I N sin (e - 

 The square of the current is given by 



i" = U + V sin* (9 - *) II N sin - 



