1464 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1953 



where $ is the final flux. This may also be written in integral form as 



. = (a + 0.— )f^/^-^,. (26) 



The change is the introduction of the exponential modifying the core 

 constant Ge. 



Fig. 25 shows comparisons of curves for four different coil to core 

 constant ratios. In each case, the actual flux rise, the older equation, 

 and the new first approximation are shown. 



For large coils (as an example on Fig. 25, Gc/Ge = 10) the actual flux 

 rise is well represented by either expression, their accuracy being within 

 1 per cent. 



For very small coils (on Fig. 25, Gc/Ge = 0.5) it is clear that the older 

 representation is never a good approximation of actual flux rise. The new 

 approximation represents the start of the dynamic flux rise quite well, 

 but is not accurate for the second half. However no single exponential 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6 



t/te 

 Fig. 24 — Flux rise curves. 



5 7.0 7.5 8.0 8.5 9.0 



