34 Dr. McLachlan on Effective Inductance, Effective 



winding o£ fixed dimensions depends chiefly on the magnetic 

 quality and behaviour of the iron. Provided the current is 

 constant and the oscillations are damped or undamped sine 

 waves, we may write approximately that L=A oy u, e , where, for 

 a given position of the rotor, L is the inductance, A^ is a 

 constant, and \x e is the effective permeability of the magnetic 

 circuit, including air-gaps. The value o£ A is approximately 

 constant for the range of f requencies in a magneto say from 

 2 X 10 s — to 10 4 ~, but the value of /x e varies with the fre- 

 quency. It is well known that the apparent permeability of 

 iron (fia) found from measurements with a coil wound on an 

 iron core in which there is no air-gap or in which the de- 

 magnetizing coefficient and leakage are very small, decreases 

 with the frequency whether the oscillations are damped or 

 undamped. The magneto circuit is one in which the magnetic 

 path is not completely wound with copper, especially in the 

 inductor type, and one in which there are several air-gaps. 

 Although the air-gaps are only a small proportion of the 

 length of the magnetic circuit, they are equivalent to a 

 length of iron fi a times that of the gap. The air-gaps do not, 

 however, alter the general behaviour of the iron qualitatively. 

 This can easily be shown approximately neglecting leakage 

 as follows : — 



Let / = mean length of magnetic circuit containing 

 air-gaps, assumed equal to length of mag- 

 netizing coil. 

 l Y = mean length of iron of circuit. 

 A = cross-sectional area of circuit assumed constant. 

 N = total flux. 

 B = N/A - apparent flux density under alternating 



current in circuit having air-gaps. 

 H = apparent magnetizing force under alternating- 

 current. 

 B/H = /x e . 



yi ai fi e = apparent permeability * and effective perme- 

 ability under alternating current. 



Then 



or 



or 



HZ 

 Rl 



= 



A^i+A^-y 



k— Pail— 1\) 



B 

 B 



He = 



Ha 



Hal 



H 



k+Ha(l-ll) 



(1) 



* When magnetic circuit is of uniform cross-section and there is no 

 air-gap. 



