Resistance, and Self-Capacity of Magneto Windings. 35 



Taking 









Pa = 



I = 



500 

 10 em., 





length of 



lir 



-gap 



I 



7 



0-03 cm.. 





we have 







Pe 





5xl0 3 







= ltM 



(500x0*0 



3) 











= 200. 







At a higher frequency assume 



A*»= 100; 

 ihen 10 3 



He = 



10 + 3 



77. 



The effect of the air-gaps is clearly greater at the lower 

 frequency owing to the higher apparent permeability of the 

 iron, or in other words the air-gap at the lower frequency is 

 equivalent to a greater length of iron than at the higher 

 frequency. As the value of fi a decreases, the proportionate 

 effect of the air-gaps decreases also. Thus the effect of the 

 .air-gaps in decreasing the effective permeability of the 

 magnetic circuit is greatest when the current is growing in 

 the primary before break, since [i a is greatest then. The 

 gaps cause a diminution in the self-inductance of the primary 

 -winding. In the above case it is of interest to observe that 

 little advantage would be gained by using an iron core in 

 which the value of fi a was 1000, since this would only 

 increase fi e to 250 ; i. e., 100 percent, increase in fi a produces 

 only 25 per cent, increase in fi e . On the other hand, increasing 

 fM a from 1C0 to 200 increases ^ from 77 to 125, i. e.&2 per 

 cent, increase. When the air-gap in the magnetic circuit is 

 proportionately large there is a considerable leakage and the 

 flux density in the gap is far from uniform. In this case we 

 may write approximately 



Ve = /*alI{h+9H<aQ- l l)U ( 2 ) 



where " g " is a variable parameter depending on the 

 frequency. When l x is small compared with gp a (}—h), 

 the expression for the effective permeability reduces to 

 li;=±ll({l-l x )g}. Since I and l x are constant it follows 

 that \ie is approximately constant and independent of thv 

 frequency, provided g is constant. The latter condition will 

 obtain at acoustic frequencies. This case corresponds ap- 

 proximately to that of a magneto in which the armature is 



J) 2 



