F *, 



u^-JLlirrrr rrm^ J 



6-A] GENERAL STUDY. 215 



The discussion of Figs. 3, 4 and 5 illustrates the application of Laws 

 (i) and (2). 



The modified form of KirchhofFs Law for current becomes: 



34. Law (5). Vector Addition of Currents: General Law. At 

 any point in an alternating current system the vector sum of the 

 currents measured all towards or all away from that point is zero; 

 such vectors form a closed polygon. 



35. Law (4}. Vector Subtraction of Currents: Special Law. At 

 any point in an alternating current system where three currents come 

 together, if one current is measured towards and the second away 

 from that point, the third current will be the vector difference of 

 the two. 



The discussion of Fig. 14 illustrates the application of Laws (3) 

 and (4). 



36. Notation. There is no universally adopted notation for poly- 

 phase circuits. The most complete and least ambiguous method is 

 to letter every junction or point on the diagram of connections and 

 to use two letters (as subscript if desired) in the proper sequence 

 to designate the vector current or electromotive force between two 

 points. Thus, from X to Y we may have electromotive forces XY 

 or EXY; in the reverse sense, YX or YX; similarly, we may speak 

 of the currents XY or /XY and YX or /YX. This makes definite the 

 direction or sign of the vector quantity in every case. In some cases, 

 particularly the simpler ones, the complete definiteness is not needed 

 (being unessential or obvious) and a single subscript is then simpler, 

 as D, s, /A, /B. In general the double-subscript notation is to be 

 recommended on account of its exactness, as illustrated in the dis- 

 cussion of Fig. 14. 



37. In applying Law ( I ) it is necessary, in order to obtain a 

 vector sum of zero in proceeding from a generator around a circuit 

 and back to the generator, to take the generated electromotive forces 

 or counter electromotive forces in each part of the circuit: thus, the 

 electromotive force produced by self-induction 90 behind the cur- 

 rent (not that to overcome self-induction 90 ahead of the current) ; 

 and the electromotive force produced by resistance, in direction 

 exactly opposite to the current (not the electromotive force to over- 

 come resistance which is in phase with current). This becomes 

 obvious upon inspection of the triangle for the electromotive forces 



