THE iniLPING-VP OF SINUSOIDAL CURRENTS 

 1 r" //x 



p= / \ s\ixt\.[Pj\)-^r(-\)] 



IT Jo n 



IT »'o A 



a= ' / vsi,WX[C»„(X) + (.U-X)l 



(ij. 



where 



PJX) = 'i^^^ COs[B(co + X)-B(a;)l, (13) 



(?„(X) = ^^^gp\sin[B(a, + X)-5(a,)l. (14) 



and.4(u.) = l/|Z(jo))|. 



These formulas are directly liediRiblu from the fad tiiat ihe ap- 

 plictl e.m.f., defined as zero for negative values of / and E cos (at for 

 t>o, can itself be expressed as 



I-'-'['+^"t--]- 



In the practically important case where B'iw) is finite, it is of ad- 

 vantage to introduce the transformation l' = t — B'(w), and to write: 



1 /"° ^x 



p=A / ''^sin/'X[rjX)+C^J-X)] 

 jr ^0 " 



_ 1 Z'" '(^ COS t'\ [ VJ\) - VJ-\)1 



T J(\ A 



<,= ' / "^ sin/'x(r„(X) + r„(-x)] 



jr»'o X 



/*" '^ cos /'X [i' (X)- i'„(-X)l. 

 «/o X 



(15) 



(10) 





r {\) = -'^;^ coi^lB[w + \)-H{o,)-\B'(w)l (17) 



^(«) 



^«(M = ^%^^sin[B(a. + X)-«(a;)-XZJ'(a;ll. (18) 



