CHAP. XII] INDUCTANCE OF WINDINGS 213 



after combining, 



. . . (144) 



This value is between two and four times as large as the 

 value given by eq. (143). For this reason, in most transformers, 

 the low-tension coil is split into two sections; compare also with 

 Fig. 14. 



Formula (143) and the values of k given above have been 

 deduced for the core-type transformer. It is clear, however, 

 that the same formulae will apply to the shell-type and the cruci- 

 form type transformers with cylindrical coils, though the coeffi- 

 cient k may have different values in each case. Until more 

 reliable and numerous experimental data are available the same 

 values of A; will have to be used for these types as for the core- 

 type. 1 



(2) Flat Coils. With flat coils (Fig. 51) the inductance of 

 a part of the winding between AB and CD can be calculated 

 in precisely the same way as in Fig. 50. If the primary winding 

 is split into q sections, the inductance per section, by analogy 

 with eq. (143), is 



W9=M/'(^i/<?) 2 Om/2/][a + J(6 1 +6 2 )]10-8henrys, . (145) 



\\-hrrc the dimension I is again measured in the direction of 

 the lines of force and O m is the mean length of a turn. The 

 dimensions a, 6^ and 6 2 are indicated in Fig. 51. The inductance 

 of the whole winding is 



. . (146) 



win -ro all the lengths are expressed in centimeters, and /i= 1.257. 



This formula presupposes that the m.m.fs. are balanced, or 

 in other words, that there are two half-sections of the same 

 winding at the ends; such is usually the case in order to reduce 

 the leakage reactance. (See also Fig. 13.) 



Eq. (146) shows that the leakage reactance is considerably 

 reduced, and consequently the voltage regulation improved, by 

 subdividing the windings and placing the primary and the 



1 See also the Standard Handbook for Electrical Engineers under Trans- 

 former, leakage reactance. 



