Alternate Current Transformer. 59 



In a similar manner we find that 



•VT AT LJ,' ^2, J^ I 



■L*Al2— iU.21— y ( 2 6 j' 



but 



.•..'ri=^,-n-g + ^jr+ 1^ |-, and similarly 



From which we see that the leakage coefficient, x.,, of the coil 

 next the core is negative. 



The equation giving .To + x-j can be written 

 x, + x,=^^{b, + b.:) (Si + S,) (I.) 



where Sj and S.^ are the mean radii of the two coils ; and if ^^ 

 and q.y be their space factors, their copper sections per unit length 

 of winding are 

 ^1^1 and ^2^2- 

 These will be equal or very nearly so, and 

 let l)^q.^=biq.,=s, 

 then bi-\-b.i-='2sjQ, 



where Q==-^i^-, the harmonic mean of q^ and q.,. 



The total copper volume 



= 27rA'(Si^/i + S2^.A)=27rX'^(Si + S2)=7rQA'(^ + A,)(Si + S2), 

 Volume of iron 



and o-=47r/u, t^ 



where A=:length of magnetic circuit, 

 hence 



K^ volume of copper 



" - 3/xQX'- volume of iron ^ 



and if the transformer is being designed so that the copper losses 

 are to be z times the iron losses at full load, then 



