CHAP. XII] INDUCTANCE OF WINDINGS 217 



a = 12 mm. Calculate the correction factor kf in formula (147). Hint: 

 Eliminate the ir drop, using the wattmeter reading. Ans. About 1.05. 



Prob. 6. What is the greatest permissible thickness of the coils 

 of a 60-cycle transformer, if the reactive drop must not be larger than 

 three times the resistance drop? The ducts a are 1 cm. The space 

 factor of the copper in each coil is 0.55. The primary coils and the 

 whole coils of the secondary are of the same thickness. fc=0.98. 

 Hint : Assume O m , I, and n v and show that they cancel out. 



Ans. 6 = 3.66 cm. 



Prob. 7. In order to provide a better cooling, and at the same 

 time save on insulation, two flat high-tension coils are frequently placed 

 side by side, with a small air-space in between, and in the same way 

 the low-tension coils may be subdivided. Show that no leakage flux 

 passes in the space between the two adjacent coils which belong to 

 the same winding, so that the inductance of the winding is not appreciably 

 increased by these spaces, and can be calculated as if these spaces did 

 not exist. 1 



Prob. 8. Compare the formulae given above and the numerical values 

 of transformer leakage reactance obtained therefrom with the formulae 

 and data given in the Standard Handbook for Electrical Engineers. Do 

 this for any transformer, the dimensions of which are available. 



Prob. 9. The equivalent reactance of a transformer is , reduced 

 to the primary circuit, and is x, reduced to the secondary circuit. All 

 the primary coils are connected in series, and all the secondary coils 

 are also in series. Show that these equivalent reactances become 

 xjc? and a?,/c, a respectively, when the primary winding is divided 

 into c t branches in parallel, and the secondary winding is divided into 

 c a branches in parallel. The division is supposed to be made in such 

 a way as to keep the m.m.fs. in the adjacent coils balanced. Hint: 

 If the equivalent reactance of one primary branch is x/, that of c t 

 branches in series is Zj-XjC/, and that of c, branches in parallel is z,'/c, 

 no matter whether the secondary coils are connected in series or in 

 parallel. 



Prob. 10. Prove that the equivalent reactance of a transformer 

 is the same, whether the coils are in series or in parallel, provided that 

 the total number of turns in series is the saint 



Note: Sometimes, because of the difficulty in using heavy con- 

 ductors, it is desirable to multiple the coils. In such case, the p:ir:ilM 

 coils must have the same number of turns, and they should be sym- 

 metrically arranged, so as to prevent exchange currents. 



66. The Equivalent Leakage Permeance of Armature Windings. 

 In certain problems relating to the design and operation of 

 electrical machinery it is necessary to calculate the inductance 



1 This fact has been verified experimentally; aee Arnold, WechscUtrom- 

 ttchnik. Vol. 2 (1910), p. 29. 



