212 THE MAGNETIC CIRCUIT [ART. 64 



All the lengths here are expressed in centimeters, and //= 1.257, 

 also a = ai -f 0% is the spacing between the coils, which is a known 

 quantity. Thus, the unknown distances a\ and 0% which enter 

 into the expressions for Lj and L 2 are eliminated from the 

 formula for the equivalent inductance. 



The coefficient A; corrects for the difference between the 

 actual linkages shown in Fig. 50 at the left, and the assumed 

 linkages shown at the right. The values of k, found from experi- 

 ments, vary within quite wide limits, depending upon the pro- 

 portions of the coils. For good modern transformers Arnold 

 gives the limits of k between 0.95 and 1.05. 1 See also eq. (147) 

 below. Formula (143) gives the inductance of one leg only; 

 the equivalent inductance of the whole transformer depends 

 upon the electrical connections between the coils. 



In designing a transformer the coils are usually arranged 

 in such a way as to reduce the leakage reactance to the least 

 possible amount. 2 Eq. (143) shows that in order to achieve 

 this result, a comparatively small number of turns must be used, 

 and the coils must be thin and long. The space a between the 

 coils must be kept as small as is compatible with the require- 

 ments for insulation and cooling. 



The usual arrangement of coils shown in Fig. 50 gives a 

 considerably smaller leakage inductance than the simpler arrange- 

 ment shown in Fig. 12. Namely, with the arrangement shown 

 in Fig. 12, the permeance of the path of the complete linkages 

 in the space between the coils is naiO m /l. This expression 

 differs from that used before in that I stands in the denominator 

 in place of 21. For the partial linkages n p =n l (x/bi), where 

 x is measured now from the edge of the primary coil, furthest 

 from the secondary coil. Thus, the primary inductance is in 

 this case 



or 



By symmetry we can write the expression for L 2 , and hence, 



E. Arnold Wechselstromtechnik (2d edition), Vol. 1., p. 561. 

 2 In some cases a considerable leakage reactance is specified as a protection 

 against violent short circuits. 



