CHAP. XII] INDUCTANCE OF WINDINGS 211 



The simplifying assumptions are (a) that the paths within and 

 between the coils are straight lines, and (6) that the reluctance 

 of the paths in the space outside the coils is negligible, because 

 the cross-section of these paths is practically unlimited. 



(1) Cylindrical Coils. We shall calculate first the primary 

 inductance of a transformer having cylindrical coils, i.e., the 

 inductance due to the linkages of the leakage flux with the 

 primary, winding. The permeance of the path of the complete 

 linkages is (P c i = fJL.aiO m /2l perms, where O m is the mean length 

 of a turn in the coil P, and a! is the radial thickness of the flux. 

 The notation is shown in the detail drawing, at the bottom of Fig. 

 50. In this expression a t O m is the mean cross-section of the 

 path, being an average between the cross-sections within the 

 spaces Pi-St and P 2 -S 2 . The length of the paths within the 

 coils is 21, and the reluctance of the paths outside the coils is 

 neglected. This path is linked with n v turns. 



Similarly, the permeance of an infinitesimal annular path 

 within the primary coil, at a distance x from its center, and 

 of a width dx, is d(P P i = fiO m dx/2l perms. This path is linked 

 with n pl =n 1 (2x/6 1 ) turns. Substituting these values into eq. 

 (106) we obtain 



In - (^O m /2l) [a, 

 or 



A-Om^O^JXai + J&i) perms ..... (141) 



By a somewhat similar reasoning we should find for the com- 

 bination of the two secondary coils, assuming them to be connected 

 electrically in series, 



perms ..... (142) 



In the operation of a transformer it is the total equivalent. 

 inductance of the two windings rcdurrd to one of tin- circuits 

 that is of importance. Sin< resistances and reactances can be 

 transferred from the primary circuit to the secondary or vice 

 versa, when multiplied ly the square of the ratio of the numbers 

 of tui t, 446), tin- equivalent inductance, reduced to the 



primary circuit, and per leg of the core, is 



henrys. . (143) 



