114 THE MAGNETIC CIRCUIT [ART. 40 



no-load saturation curve is used for this purpose, assuming that 

 the leakage factor is the same at full load as at no load. However 

 careful designers sometimes plot a separate curve, using a higher 

 leakage factor, for use at full load. 



Prob. 8. Assume in the illustrative example given in the text the 

 armature current to be leading, so that the voltage drop in the armature 

 is negative and the armature reaction strengthens the field. Show that 

 with the same value of the armature current the leakage factor is about 

 1.09. 



Prob. 9. Draw rough sketches of the magnetic circuits of two 

 machines, one possessing such proportions, number and shape of poles 

 as to give a particularly low leakage factor, the other markedly deficient 

 in this respect. 



Prob. 10. Calculate the leakage factor and the leakage permeance 

 per pole of a six-pole turbo-alternator of the following dimensions; the 

 bore is 1.2 m.; the axial length of the poles 0.6 m.; minimum air-gap 

 1 cm.; maximum air-gap 2 cm.; total height of the pole 23 cm.; the 

 height of the pole-waist 18 cm. ; the breadth across the pole-waist 25 cm.; 

 that across the pole-tips 36 cm. The reluctance of the useful path in 

 the air-gap and in the armature is estimated to be about 0.57 millirel 

 per pole. Ans. 1.115; about 200 perms. 



Prob. 11. The leakage factor of the machine specified in the pre- 

 ceding problem was found from an experiment to be 1.13, at no-load, 

 when the total flux per pole was 20.35 megalines. What is the true 

 leakage permeance if 20 kiloampere-turns were required at that flux for 

 the air-gaps and the armature, per pair of poles ? Ans. 234 perms. 



Prob. 12. The machine specified in the two foregoing problems 

 requires at full load 20 per cent more ampere-turns for the air-gap and 

 armature, on account of the induced voltage being 12 per cent higher 

 than at no-load. The armature reaction amounts to 4000 demagnetizing 

 ampere-turns per pole. What is the leakage factor at full load, according 

 to the calculated leakage permeance and according to that obtained 

 from the test? Ans. 1.16; 1.19. 



Prob. 13. A closed electric circuit consisting of a battery and of 

 a bare conductor is immersed in a slightly conducting liquid, so that part 

 of the current flows through the liquid. Indicate the common points 

 and the difference between this arrangement and a magnetic circuit 

 with leakage. Using the electrical analogy, show that armature reaction 

 increases the leakage factor; also explain the fact that, in order to com- 

 pensate for the action of M demagnetizing ampere-turns on the armature, 

 more than M additional ampere-turns are required on the pole-pieces. 



Prob. 14. In some books the permeance between two pole-faces 

 (Fig. 30) is calculated by assuming the lines of force to be concentric 

 semicircles as shown by the dotted lines. Show that such a permeance 

 is smaller than that according to formula (57) and therefore should not 

 be used. Hint: Compare the lengths of two corresponding lines of 

 force. 



