216 THE MAGNETIC CIRCUIT [ART. 64 



we get the coefficient J, which appears in eq. (143). In eq. 

 (143) rij and L^ refer to the double leakage coil. Substituting 

 in eq. (144) Jnj for n x and ^L^ for L^, we get eq. (143). Thus, 

 the differences between the two equations is readily explained. 

 In case the coils are divided in any unusual manner, we must 

 first locate the hearts by noticing where the m.m.fs. are balanced. 

 Then we should figure out the inductance by eq. (144) for each 

 leakage coil separately. The only precaution to be observed is 

 that the various quantities refer to the leakage coil. Finally 

 (if the coils are in series) we should add the various induct- 

 ances together. The arrangement with half coils on the ends 

 gives the minimum of inductance for a given number of coils. 



Prob. 1. The approximate assumed dimensions of a 1 5-kw., 2200/1 1 0- 

 v., 60-cycle, cruciform-type transformer with cylindrical coils (Fig. 14) 

 are: O m = 140 cm.; b 1 =4.5 cm.;*6 2 = 3 cm.; a = l cm. The maximum 

 useful flux is 1.03 megalines. Show that the relationship between the 

 height I of the winding and the percentage reactive voltage drop is 

 zJ = 166. Assume k = 1.10. 



Prob. 2. Referring to the preceding problem, what is the permeance 

 of the space between % the outside low-tension coil and the high-tension 

 coil, per centimeter of the height of the coils, and what is the effective 

 value of the flux density in this space, at full load ? 



Ans. 197.5 perms per cm., 3420/J lines per sq.cm. 



Prob. 3. Each leg of a core-type transformer is provided with six 

 flat high-tension coils of 530 turns each, interposed with the same 

 number of low-tension coils of 40 turns each, one of the low-tension 

 coils being split in two and placed at the ends. The high-tension coils 

 are wound of 3 mm. round wire, 53 layers, 10 turns per layer (61 = 3 cm.) ; 

 the low-tension coils are wound of 8 mm. square wire, in 20 layers, 2 turns 

 per layer (6 2 = 1.6 cm.). The distance between the coils is 20 mm. 

 Taking the inductance of this transformer to be unity, calculate the 

 relative inductances of the transformer when the high-tension winding 

 is divided into three coils and also into two coils, assuming k, I, and 

 a to be the same in all cases. Ans. 2.55 ; 4.66. 



Prob. 4. Solve the preceding problem, taking into account the 

 change in k. Ans. 2.42; 4.14. 



Prob. 6. The following results were obtained from a short-circuit 

 test on a 22/2-kv., 2500-kva., 60-cycle, shell-type transformer, with 

 flat coils: With the high-tension winding short-circuited, and full rated 

 current flowing through the low-tension winding the voltage across 

 the secondary terminals was 73.5 v., and the wattmeter reading was 

 '27 kw. The transformer winding consists of 12 high-tension coils of 

 100 turns each, and of 11 low-tension coils interposed between the 

 high-tension coils, together with 2 half-coils at the ends. The dimen- 

 sions of the coils are : O m =2.6 m. ; I = 18 cm. ; 6 X = 16 mm. ; 6 2 = 10 mm. ; 



