Page 16 - Solutions Manual to accompany Electric Machinery Fundamentals

The two coils on this core are wound so that their magnetomotive forces are additive, so the total
magnetomotive force on this core is

 F Ni   N i  600 t 0.5 A   200 t 1.00 A  500 A t 
TOT 1 1 2 2
Therefore, the magnetizing intensity H is

H  F  500 A t  192 A t/m

l c 2.60 m
From the magnetization curve,
B  0.17 T

and the total flux in the core is
 TOT   BA  0.17 T  0.15 m  0.15 m  0.00383 Wb

The relative permeability of the core can be found from the reluctance as follows:
F l
R  TOT 
 TOT  r  0 A

Solving for µ yields
r

 l  0.00383 Wb 2.6 m 
  r TOT   704
F TOT 0 A   500 A t    10 -7 4   H/m 0.15 m  0.15 m
The assumption that  = 1200 is not very good here. It is not very good in general.
r
1-13. A core with three legs is shown in Figure P1-10. Its depth is 5 cm, and there are 400 turns on the center
leg. The remaining dimensions are shown in the figure. The core is composed of a steel having the
magnetization curve shown in Figure 1-10c. Answer the following questions about this core:
(a) What current is required to produce a flux density of 0.5 T in the central leg of the core?
(b) What current is required to produce a flux density of 1.0 T in the central leg of the core? Is it twice
the current in part (a)?
(c) What are the reluctances of the central and right legs of the core under the conditions in part (a)?

(d) What are the reluctances of the central and right legs of the core under the conditions in part (b)?
(e) What conclusion can you make about reluctances in real magnetic cores?

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