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452 ⏐⏐⏐ MAGNETIC CIRCUITS
Section � (Wb) A (m 2 ) B (T) H (At/m) l (m) Hl (At)
abcda 1.5 � 10 �5
(a)
(b)
� c
� c
� c
� c
� c
� 1
�
� abcda
(a)
� 2
0.15 � 10 �3
E 1
TABLE 11.5
The flux density throughout is
B � � �
A � � �10 � 10�2 1.5 � 10
T � 0.10 T
and
1
H (from Fig. 11.24) � �(100 At/m) � 20 At/m
5
Applying Ampère’s circuital law,
N1I1 � N2I2 � Habcdalabcda (60 t)(2 A) � (30 t)(I2) � (20 At/m)(0.16 m)
120 At � (30 t)I2 � 3.2 At
and (30 t)I2 � 120 At � 3.2 At
116.8 At
or I2 ���3.89 A
30 t
�5 Wb
���3
2
0.15 � 10 m
For the analysis of most transformer systems, the equation N 1I 1 �
N 2I 2 is employed. This would result in 4 A versus 3.89 A above. This
difference is normally ignored, however, and the equation N 1I 1 � N 2I 2
considered exact.
Because of the nonlinearity of the B-H curve, it is not possible to
apply superposition to magnetic circuits; that is, in Example 11.5, we
cannot consider the effects of each source independently and then find
the total effects by using superposition.
11.12 AIR GAPS
I
R abcda
FIG. 11.34
(a) Magnetic circuit equivalent and (b) electric circuit analogy for the
transformer of Fig. 11.33.
Air gap
FIG. 11.35
Air gaps: (a) with fringing; (b) ideal.
(b)
0.16
Before continuing with the illustrative examples, let us consider the
effects that an air gap has on a magnetic circuit. Note the presence of
air gaps in the magnetic circuits of the motor and meter of Fig. 11.11.
The spreading of the flux lines outside the common area of the core for
the air gap in Fig. 11.35(a) is known as fringing. For our purposes, we
shall neglect this effect and assume the flux distribution to be as in Fig.
11.35(b).
E 2