Page 18 - Solutions Manual to accompany Electric Machinery Fundamentals

The magnetizing intensity H required to produce a flux density of 0.50 T can be found from Figure 1-10c.
It is 75 A·t/m. Similarly, the magnetizing intensity H required to produce a flux density of 1.00 T is
about 160 A·t/m. Therefore, the total MMF needed is

I
I
F TOT  H center center  H outer outer
F TOT  160 A t/m 0.21 m   75 A t/m  0.63 m  80.8 A t 
and the required current is

 80.8 A t

i  TOT   0.202 A
N 400 t
This current is not twice the current in part (a).

(c) The reluctance of the central leg of the core under the conditions of part (a) is:

F   75 A t/m 0.21 m 

 R TOT   12.6 kA t/Wb
cent  TOT 0.00125 Wb
The reluctance of the right leg of the core under the conditions of part (a) is:

F 50 A t/m 0.63 m  

 R TOT   50.4 kA t/Wb
right
 TOT 0.000625 Wb
(d) The reluctance of the central leg of the core under the conditions of part (b) is:

F   160 A t/m 0.21 m 

 R TOT   13.4 kA t/Wb
cent
 TOT 0.0025 Wb
The reluctance of the right leg of the core under the conditions of part (b) is:
F 75 A t/m 0.63 m 

 R TOT   37.8 kA t/Wb
right  TOT 0.00125 Wb
(e) The reluctances in real magnetic cores are not constant.
1-14. A two-legged magnetic core with an air gap is shown in Figure P1-11. The depth of the core is 5 cm, the
length of the air gap in the core is 0.05 cm, and the number of turns on the coil is 1000. The
magnetization curve of the core material is shown in Figure P1-9. Assume a 5 percent increase in
effective air-gap area to account for fringing. How much current is required to produce an air-gap flux
density of 0.5 T? What are the flux densities of the four sides of the core at that current? What is the total
flux present in the air gap?

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