92 



BILI.L SYSTliM TI.CIISICAL JOLRX.IL 



mutual inductaiu-f la-lwccii .iin two coils changes sign, the signs ae- 

 comjianying that mutual inductance in the ahoxe formulae are 

 reverse! 1. 



M'„ m'„ 



(A) (B) 



Fig. 34 — Kciulvalent t Networks of Inductance 



Similarly, the ir networks of Fig. 34 are also poteniialK ci|ui\.iUni 

 The formulae governing their equivalence are 



A = f . 



^"= z; • 



I^C = — 



in w liich — 





i. 

 La" Lb" 



La" + Lb"+Lc 



Lb"Lc" 

 La" + Lb"+Lc 



La"Lc" 



r,=FA/(2. 



r,=F-U23, 



La" + Lb" + Lc 



r,^M[s, 



\vh 



La" = Li'±M{2±M\3, 



Lb" = Li ± M12 ± M23, 

 Lc"=L,'±M'y.,±M:,,. 



(83) 

 (84) 

 (85) 



(86) 

 (87) 

 (88) 



(89) 

 (90) 

 (91) 



As in the preceding case, the upper of the two signs occurs with the 

 series aiding mutual inductance between all the pairs of coils. \\ hen 

 the mutual inductance between any two coils changes sign, the signs 

 acct)mpan\ing thai nnitual inductance in the above formulae are 

 re verse* I. 



At least two of the three inductances (in Fig. 33M or in I'ig. 34B) 

 will alw.iNs be positive in sign while the third inductance may be 



