Page 20 - Solutions Manual to accompany Electric Machinery Fundamentals

 0.00131 Wb
B    0.524 T
right  
A 0.05 m 0.05 m
The flux density in the other three legs of the core is
 0.00131 Wb
B  B  B    0.262 T

left
bottom
top
A  0.10 m 0.05 m 
The magnetizing intensity required to produce a flux density of 0.5 T in the air gap can be found from the
equation B   o H :
ag
ag
B 0.5 T

H  ag  ag  4  10  7 H/m  398 kA t/m
0
The magnetizing intensity required to produce a flux density of 0.524 T in the right-hand leg of the core
can be found from Figure P1-9 to be

H right  410 A t/m
The magnetizing intensity required to produce a flux density of 0.262 T in the top, left, and bottom legs of
the core can be found from Figure P1-9 to be

H top  H left  H bottom  240 A t/m
The total MMF required to produce the flux is

 F H l  H l  H l  H l  H l
TOT ag ag right right top top left left bottom bottom


F    398 kA t/m 0.0005 m   410 A t/m 0.40 m   3 240 A t/m   0.40 m
TOT



 F 278.6 164 288 651 A t 
TOT
and the required current is

i  F TOT  651 A t  0.651 A
N 1000 t
The flux densities in the four sides of the core and the total flux present in the air gap were calculated
above.
1-15. A transformer core with an effective mean path length of 6 in has a 200-turn coil wrapped around one leg.
2
Its cross-sectional area is 0.25 in , and its magnetization curve is shown in Figure 1-10c. If current of 0.3
A is flowing in the coil, what is the total flux in the core? What is the flux density?

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