INSTRUMENT TRANSFORMERS 583 



Naturally the inductances L L and L 2 are made as small as 

 possible; if they could be entirely neglected, 



tan j8 = ^- 



The same results may be more simply derived by use of a vec- 

 tor diagram, Fig. 360. Take 7 2 along the horizontal axis, and 

 assume that the condition of balance has been attained. 



v. 



\>. 



FHJ. 360. Vector diagram for Fig. 358. 



At balance the lM). ca must equal the P.D. dc (see Fig. 358); 

 that is, the points a and c in Fig. 360 must coincide; so 



a - m = !! 

 /, = \!& + co 2 (L 2 --m) 2 

 ' Jj V #i 2 + <o 2 Li 2 



When a and c coincide, 



tan = tan (a -f 6). 



co (L/2 m) 

 tail a = ^-4= - 



LI co 



tan - -w- 

 Hi 



co(L 2 - 



L 



[CO 



1 



CO' 



- m) 



- a)Ri (L 2 m) 

 \- co 2 Li (L 2 - m) 



With good transformers the quantity m is small; both R i and R 2 

 are non-inductive, so called. Though reduced to a minimum, LI 

 and L 2 may be of importance when phase angles are determined. 



