796 



Dr. H. H. Poole on Vector Methods for 



In comparing two mutual inductances, there are evidently 

 four possible arrangements, as we can interchange the pri- 

 mary and secondary of either coil. .We see that it is 

 generally best to use the low-inductance side of each coil 

 as secondary except in the case where some other arrange- 

 ment would make the ratio of the secondary self-inductances 

 near th« desired value. 



Comparison of a Mutual with a Self-Inductance 

 [Maxwell's Method'] . 



Rk. a. 



Circuit Diagram 



Since A x and A 2 are at the same potential, c x and c 2 are 

 evidently in phase, so the current in the primary of M 

 is c 1 + c 2 . The vector diagram is obviously as shown, being- 

 identical with fig. 1 as far as the branch OA 2 B is concerned. 

 In the branch OAxB we have a driving E.M.F., (cj -f c 2 )Ma), 

 represented by BQ. This must be subtracted from the fall 

 of potential c^co [PQ], with which it is in phase. The 

 difference must be equal to c 2 L 2 a>. 



Hence 



c i r 1 = c 2 r 2 

 c 1 R 1 = c 2 R 2 

 c^Liw = c 2 L 2 co + (ci -+ c 2 )JSlw 



J) L r M 

 ~R 2 L 2 + M' 



In'=^L,+ 



ro 



( 1+ S) 



M. 



In the Campbell Indactometer Bridge, as used with 

 unequal arms for measuring large self-inductances, the 

 inductance L to be measured is inserted in series with 

 the secondary L' of the mutual coil, so that L X = L + L'. 



