M.\r,xi;Tir ni:sir,\ (if ijklavs 



i)i 



Kcnnelly rolation descrilx'd in SiM-tioii I. A solulioii lo the i-csultinji; 

 equations can be obtained in scries t'urni, \m\ this solution is too complex 

 for convenient use in enjiiinccrinjj; estimates. From this formulation of 

 the j)i'oiilem, howex'ci-. it is ai)i)ai('iit that tlie use of lumjx'd values of 

 core and leakaj;e reluctances at hi^h densities (an only he a rougli ap- 

 proximation, as the reluctance per unit length must vary along the core, 

 and the pattern of the leakage field and lience the leakage reluctance are 

 no longer constant. However, in representing the core reluctance as 

 increasing from its low density \alue and approaching infinity as v? — ^ ^p", 

 th(> lumped approximation correctly represents the limiting conditions. 

 It therefore* provides a rough approximation to the intermediate values. 



Series-Parallel Magnetic Circuit 



Subject to the limitations discussed above, the magnetic circuit of most 

 ordinary electromagnets can be represented in the form shown in Fig. 21. 

 The core reluctance (Re is in series with two parallel paths: a leakage path 

 of reluctance (Rl2 , and an armature path of reluctance (R02 + x/A-2 . The 

 subscript 2 is used with the constants of this particular circuit to dis- 

 tinguish them from those of the simpler approximation to be discussed 

 below. The magnetic circuit of Fig. 3 reduces to that of Fig. 21 if the 

 reluctance (R^ of the former is ignored, or considered as part of the 

 reluctance (Ros- 



The circuit reluctance (ft, or J/V, tan be derived from the circuit by 

 the procedure applying to resistances in an electrical circuit, and is given 

 bv: 



(Rls 



(R = (Re + 



(^«^ + £) 



(23) 



(R/.2 + (R,r> + 



A, 



The evaluation of the constants of this circuit may be desci'ibed with 



Fit;. 21 — Series parallel magnetic (•ireuit — tlic u.sual design analogy 



