Winding of Alternate-Current Electromagnets. 573 



It is, however, doubtful, since the magnetic circuit contains 

 two joints, whether so high a value as 2000 can be expected 

 in ordinary work for //,. In that case the coefficient 1*41 will 

 be lower. With the electromagnet described above, at a fre- 

 quency n = 93, and with the armature in contact, the coefficient 

 was 0'6 instead of 1*41. This is tantamount to saying that 

 the working permeability was only 850. As so arranged, L 

 being 0'044, the inductance ph was 25*26 ohms, and R was 

 0'15 ohm. The alternate voltage ratio was therefore about 170. 



As the armature was removed from proximity to the poles 

 the self-induction, and therefore the impedance, fell, making 

 the voltage ratio for equal currents lower. When the armature 

 was at 3*17 millim. the voltage ratio fell to 34, and at 9*52 

 millim. to 21*5. 



It was stated above that in ordinary cases the ratio pL/R 

 might be taken instead of the more complete expression of 

 equation (6) . If it is desired to obtain a nearer approxima- 

 tion to */R 2 -f^> 2 L 2 /;R than is afforded by simply neglecting 

 the R under the square-root sign, we may take the value 



V« _ ph , R 



V c ~ R ' 2pL> 



which, by reference to the preceding numerical instances, 

 shows that the correcting term is really negligible, being in 

 the first case, where pL/R was 170, only 3^, and in the 

 last case, where pL/R was 21*5, only ^3, less than -J- of 1 per 

 cent. 



8. [Added April 27f/i.] — Lastly, a very simple expression can 

 be found for the number of windings, in terms of any desired 

 mean value of the magnetic flux N in the iron. For if the 

 iron of cross-section A is subjected to cycles of magnetization 

 in which the mean value of the permeation is B, the mean 

 flux is N = AB, and if the frequency be n periods per second, 

 the self-induced electromotive force in W windings surround- 

 ing the iron will be equal to 27rnWN-7-10 8 volts. If, then, 

 the resistance is negligibly small, this may be equated to V, 

 the mean volts of supply, whence we obtain at once 



Vx 10 8 

 w = ^xiu 



pa 



For example : — Suppose that in the above magnet it were 

 desired to obtain a permeation of 4000 lines to the square 

 centimetre, the total number of lines N would equal the area 

 A (6*5 square centim.) multiplied by 4000, or N = 26,000. 

 Taking the volts as 50, and the periods per second as 93, we 

 find by formula (9), W = 329. 



Phil. Mag. S. 5. Vol. 37. No. 229. June 1894. 2 R 



