180 ELECTRICAL ENGINEERING 



or, substituting the values of n and r z found above, 



T T di ..T 



(I c + i)r c _ + n + L ~-r = (I 9 i)i 



and 



This equation cannot be solved easily. Due to the effect of 

 self-inductance the current i does not decrease so quickly as in 

 curve (1) but follows curve (3), shown in Fig. 145. It will not 



T 



have fallen to zero at time i ~ and will have grown to a value 







ii less than I c at time t = T. Commutation will therefore not be 

 complete and when the brush breaks contact with bar 1 the current 

 I c ii from coil 6 will try to jump across to the brush and will 

 cause a spark. 



In order to reverse the current completely in the time T it is 

 necessary to have an e.m.f. generated in the coil to assist com- 

 mutation. The brushes of a generator are therefore moved ahead 

 in the direction of rotation so that the coil when short circuited 

 is cutting the fringe of lines from the pole tip. 



The intensity of this field is not constant but increases as the 

 conductor approaches the pole tip; therefore, the e.m.f. produced 

 by it also varies. 



If at the time represented in Fig. 144 there is an e.m.f. e gen- 

 erated in the coil assisting commutation, equation 206 can be 

 written 



This equation cannot be solved in general but it is possible to de- 

 termine the value of e required at any instant to cause the current 

 to vary as a linear function of time from I c to I c in the time T. 

 On this assumption 



T T -2t 

 Ic-- 



and 



(ti = _27 



dt ' T' 



