GENERAL THEORY OF THE TRANSFORMER. 241 



119. Calculation of leakage inductance P. The value of the 

 inductance-equivalent of the magnetic leakage of a transformer 

 depends upon the size and shape of the primary and secondary 

 coils, and it is very small when the windings are arranged in 

 alternate sections of primary and secondary as described in Art. 

 97. The calculation of the inductance-equivalent of magnetic 

 leakage would be very simple if the whole of the leakage flux, 

 / -f s in Fig. 205, passed between the primary and secondary 

 coils and no portion of it passed through the region occupied by 

 the winding's of wire : but in an actual transformer the two coils 



o 



are always placed as near together as possible, and nearly the 

 whole of the leakage flux passes across the region occupied by 

 the windings. We shall, however, calculate the value of the 

 leakage inductance P on the basis of the idea that all of the 

 leakage flux /, Fig. 205, encircles all of the primary turns, and 

 that all of the leakage flux s, Fig. 205, encircles all of the sec- 

 ondary turns ; and, in calculating the total leakage flux, / -f s, 

 on this basis, we shall count only I /nih part of any portion of 

 leakage flux which encircles I /nth of either coil. Thus <j> lines 

 of flux encircling one half of one of the transformer coils is equiv- 

 alent to </2 lines of flux encircling the whole coil. 



When we shall have calculated the total leakage flux, / -f- s 

 (which is represented by the line ba, Fig. 206, and which is to 

 be thought of as encircling the primary coil), due to a given 

 value, z 7 , of current in the primary coil and a corresponding 

 current, i n (= z 7 x N r /N"), in the secondary coil, then the 

 product of the leakage flux, p -f s, times the number of primary 

 turns N 1 is equal to the product of the inductance P times 

 the current z 7 , as explained in Appendix A, so that 



In the following discussion it is convenient to consider the 

 total leakage flux / -f s in three parts, namely, the part 4>' 

 which depends upon the flux which passes through the region 



