Question

Example 3.4 The reluctances of the three air gaps shown in Figure 3.14 are Ri = 3 x 109, R2 = 2 x 100, and R3 = 2 x 100, all in At/Wb. a) Draw the magnetic equivalent circuit and write the loop equations. b) Compute the flux linkages X, and X, and find Li, L2, and M. M = 0 * N, = 100 Permeability of iron = U=00 N, = 100 u = 0 Figure 3.14: A coupled magnetic circuit for Example 3.4

Answer 1

4 = 2 Perme cability N, 2100 Qirm = 0 ly=0 BN2=100 We know that Reluctane (R) is given by clc R² Molly Ac. de = Mem cone length & Ac Area of cross section. oo ch a o oo R 0.

R {3x106 2x106 Rs Prz 2x106 let a=0 a = 2 Nip, = Rz (d. – 22) Nilz & P2 R2 = f (d.-8. ). (6) from above two equation me Con calculate 8, e di Q- Q = Nili - R38, +(23-Pr) d = Neiz - Multiply by – R & add it with equation o - R Q - R = Nit - R₂8, et (Roz-R) d = N212 da (-R - B + R) = 11, -N212

Nii – U12 -R FRL 100 (11-12) (-2X2 + 3) 106 10-4 (1-12) 02 = (12-1) 210-3 Woe 10-3 we : 0 = (1-1) e totes meus To lipoli 210*+ Hoya 1ooli 2x106 20 riidz til 37 Widz til mu -4, 20 100 (31-22) mH. Noi - 100 (311-21 ) MH. La 100 (21) 1012 mni Nace – 1012