CHAP. V] EXCITING AMPERE-TURNS 81 



assume first that the maximum flux density in the core is so 

 low, that it lies practically on the straight part of the mag- 

 netization curve of the material (Fig. 3). The case of high flux 

 densities is considered in the next article. 



Since by assumption the instantaneous magnetomotive forces 

 are proportional to the corresponding flux densities, the magnetiz- 

 ing current must vary according to the sine law. It is sufficient, 

 therefore, to calculate the maximum value of the magnetomotive 

 force, corresponding to the maximum flux. Knowing the ampli- 

 tude m of the flux and" the net cross-section of the core, A, the 

 flux density B m becomes known; from the magnetization curve of 

 the material (Fig. 3) the corresponding value of H m , or the ampere- 

 turns per unit length of path, is found. The mean length I of the 

 lines of force is determined from the drawing of the core, so that 

 the total magnetizing ampere-turns M m = H m l can be calculated. 

 The mean magnetic path around the corners is somewhat shorter 

 than the mean geometric path. 



Let n\ be the number of turns in the primary winding, and i 

 the effective value of the reactive component of the exciting cur- 

 rent. We have then 



M m ........ (41) 



From this equation the quantity which is unknown can be calcu- 

 lated. 



It is presupposed in the above deduction that the joints 

 between the laminations offer no reluctance. In reality, 

 the contact reluctance is appreciable; its value depends upon 

 the character of the joints, and the care exercised in the 

 assembling of the core. This reluctance of the joints can be 

 expressed by the length of an equivalent air-gap having the same 

 reluctance. Thus, experiments show that each overlapping joint 

 is equivalent to an air-gap 0.04 mm. long. A butt joint, with 

 very careful workmanship, is equivalent to an air-gap of about 

 0.05 mm. ; in practice, a butt joint may offer a reluctance of from 

 60 to 100 per cent higher than the foregoing value. 1 Knowing the 



1 II Holil... "Maim. -tic Reluctance of Joints in Transforming Iron, "Journal 



1.) lnt. I -,0i., Vol. 41, 1908, p. 527. It is convenient to 



p<!iinfite the influence of the joints in ampere-turns at a standard flux 



r cuh lap joint 32 ampere-turns must be added nt a density 



of 10 kilolincs per square centimeter, while a butt joint requires at the 



