MUTUALLY BEACTIVE CIKCUITS IN PARALLEL. 69 



and the component at right angles to e, or the wattless compo- 

 nent, as it is called, is 



Adding equations (25), we get 

 (P + JcQ)i = { ri + r a 

 and multiplying this throughout by 



4- s 2 - 



it becomes 

 [P(ri + r a ) + <2<>i + * 2 - 2^f) - A; [P(s 1 + s 2 - 2^7) - Q(r, + r a )}]t 



which shows that the equivalent resistance .#, and reactance $, of 

 the parallel circuit are given by 



_ 1a - 1 a - ' 



" (n + r 2 ) 2 + ( 8l 4- s 2 - 2^) 2 ' 



and the equivalent impedance / is given by 



/ a = J2 2 4- S 2 



^ _^ __ P 2 ^^ 



~ (n + ra) 31 + (si + S 2 - 2p jf ) 



or putting in the values of P and $ 



c. _ 



r = / j 



Vt 



49. We will complete the present chapter by another example 

 of the use of vector algebra, which is both interesting and in- 

 structive. 



Two Circuits, one containing- Resistance and 

 Self-induction, and the other Resistance and 



