(JH. Xil ARMATUKE REACTION 285 



circuit is called the tension due to self-induction. If 



- is the rate at which the current is changing, the tension 

 dt 



opposing the change, which is the measure of the tendency 

 to persist, can be written : 



e = L ( jW- volts (118). 



out 



where dc is measured in amperes, and L is a constant 

 called the co-efficient of self-induction, here measured in 

 henries, the practical unit of self-induction. 



If S is the number of turns in the coil, and p the 

 permeance of the magnetic circuit surrounding the coil, 

 measured in centimetres, L=4>7rS 2 p. Further, if 9 is the 

 angular width of the brush minus that of one insulation, 

 and if the armature is rotating at n revolutions per second, 



we have - C = -y , since the current has to be changed 

 dt u 



from +i to i during the time in which the forward tip 

 of any one segment moves through an angular distance of 

 degrees. 



We can balance the tension due to self-induction by 

 causing the coil to pass at the same time in a magnetic 

 field giving rise to an induced tension in the coil of 

 equal amount but of opposite sign. If H is the intensity of 

 this field per square centimetre, the lines cut by the coil 



during the time of commutation will be , where I is 



oou 



the length of the armature parallel to the shaft and d its 

 diameter in centimetres. These lines are cut in time 



=- n seconds, hence the induced tension is TrdHlnW~ s volts. 

 6 



