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SECTION 11.8 Hysteresis
9. For the series magnetic circuit of Fig. 11.59, determine
the current I necessary to establish the indicated flux.
10. Find the current necessary to establish a flux of ��3 �
10 �4 Wb in the series magnetic circuit of Fig. 11.60.
I
N = 75 turns
I
Φ
Φ
FIG. 11.59
Problem 9.
Area (throughout)
= 3 × 10 –3 m 2
Cast iron
Φ = 10 × 10 –4 Wb
Mean length = 0.2 m
11. a. Find the number of turns N 1 required to establish a
flux ��12 � 10 �4 Wb in the magnetic circuit of
Fig. 11.61.
b. Find the permeability m of the material.
12. a. Find the mmf (NI) required to establish a flux � �
80,000 lines in the magnetic circuit of Fig. 11.62.
b. Find the permeability of each material.
I =
2 A
N 1
Φ
l m
Cast steel
I = 1 A
N 2 = 30 turns
Area = 0.0012 m 2
l m (mean length) = 0.2 m
FIG. 11.61
Problem 11.
*13. For the series magnetic circuit of Fig. 11.63 with two
impressed sources of magnetic “pressure,” determine the
current I. Each applied mmf establishes a flux pattern in
the clockwise direction.
N
I
Cast iron
l iron core = l steel core = 0.3 m
Area (throughout) = 5 � 10 –4 m 2
N = 100 turns
NI
FIG. 11.60
Problem 10.
l cast steel = 5.5 in.
l sheet steel = 0.5 in.
FIG. 11.62
Problem 12.
PROBLEMS ⏐⏐⏐ 469
Cast steel
Sheet steel
Sheet steel
Uniform area
(throughout)
= 1 in. 2
Cast steel
I
I
Φ = 0.8 � 10 I
–4 Wb N1 = 20 turns N2 = 30 turns
l cast steel = 5.5 in.
l cast iron = 2.5 in.
Area (throughout) = 0.25 in. 2
FIG. 11.63
Problem 13.
Cast iron