190 ELEMENTS OF ELECTRICAL ENGINEERING. 



the expression for the instantaneous value of this current is V 2/ n cos w/. 



When the conductor c is at brush P, w/=:(9o a), when the conductor c 

 reaches brush b, ut= (270 a), and when conductor c reaches brush again 

 w/=r(45o a), and so on. Each time the conductor c passes a brush the direct 

 current 7 /2 (discussion applies to a 2-pole machine) in conductor c is reversed. 

 Therefore the total current in conductor c is 



i= 1/2/nCOSW/zb (i) 



The -\- sign is to be taken between ut= (90 a) and /= (270* a), the 

 sign is to be taken between w/= (270 a) and ut= (450 -a), the -j- sign 

 again between (450 a) and (630 a), and so on. The angle a determines 

 simply the phase of the alternating current in the conductor at the instant that the 

 direct current is reversed. 



The meaning of equation (i) is made more clear perhaps by the curves shown in 

 Figs. 158 and 159. The upper curves in each figure are the component current 

 curves ; that is, the ordinates of the square-wave curve represent that part of the cur- 

 rent in the given conductor which depends upon the direct-current output of the 

 machine, and the ordinates of the sine curve represent that part of the current in the 

 given conductor which depends upon the alternating-current intake of the machine. 

 The alternating currents are assumed to be exactly opposite in phase to the alternating 

 electromotive forces of the machine. 



94. The heating of the armature conductors of a rotary converter. Equation 

 (i) Art. 93 expresses the instantaneous value of the actual current in a given armature 

 conductor of a rotary converter during the time that this conductor is passing from one 

 direct-current brush to the other ; that is, from uf = (90 -f- a) to w/=: (90 a). 

 The current passes through a similar set of values during the next half revolution of 

 the armature. The average rate at which heat is generated in the given conductor is 

 proportional to the average value of z 2 [equation (i) Art. 93] during the time 



