Page 17 - Solutions Manual to accompany Electric Machinery Fundamentals

SOLUTION The magnetization curve for this core is shown below:

(a) A flux density of 0.5 T in the central core corresponds to a total flux of
 TOT   BA   0.5 T  0.05 m  0.05 m  0.00125 Wb

By symmetry, the flux in each of the two outer legs must be     0.000625 Wb , and the flux density
2
1
in the other legs must be
0.000625 Wb
B  1 B  2  0.05 m  0.05 m  0.25 T

The magnetizing intensity H required to produce a flux density of 0.25 T can be found from Figure 1-10c.
It is 50 A·t/m. Similarly, the magnetizing intensity H required to produce a flux density of 0.50 T is 75
A·t/m. The mean length of the center leg is 21 cm and the mean length of each outer leg is 63 dm, so the
total MMF needed is

F TOT  H center l center  H outer l outer
 F   75 A t/m   0.21 m   50 A t/m 0.63 m  47.3 A t 
TOT
and the required current is

i  F TOT  47.3 A t  0.12 A
N 400 t
(b) A flux density of 1.0 T in the central core corresponds to a total flux of

 TOT  BA  1.0 T 0.05 m 0.05 m  0.0025 Wb

By symmetry, the flux in each of the two outer legs must be     0.00125 Wb, and the flux density in
2
1
the other legs must be
0.00125 Wb
B  1 B  2  0.05 m  0.05 m  0.50 T

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