11.3 TRANSFORMER EQUIVALENT CIRCUITS 479
Given=NI= 500 × 4 =2000 At,g 1 =g 2 = 0 .25 cm, andg 3 = 0 .4 cm;A 1 =A 2 =
0. 5 A 3 ;μ 1 =μ 2 =μ 3 =μ 0 ;φ 3 =φ 1 +φ 2 ; andH 1 g 1 +H 3 g 3 =H 2 g 2 +H 3 g 3 ==2000, we
have
H 1 g 1 =H 2 g 2 or H 1 =H 2
sinceg 1 =g 2. Thus,B 1 =B 2 , sinceμ 1 =μ 2 =μ 0. BecauseA 1 =A 2 , it follows thatφ 1 =φ 2
andφ 3 = 2 φ 1. ButB 3 =φ 3 / 2 A 1 =B 1. Thus,
B 1 =B 2 =B 3 ; H 1 =H 2 =H 3
We hadH 1 g 1 +H 3 g 3 =2000, which is rewritten as
B 1
μ 0
( 0. 25 × 10 −^2 )+
B 1
μ 0
( 0. 4 × 10 −^2 )= 2000
or,
B 1 =
2000 × 4 π× 10 −^7
0. 65 × 10 −^2
= 0 .387 T=B 2 =B 3
g 1 g 3 g 2
(a)
A 3
A 1 A 2
Figure E11.2.2
φ 1 φ 2
φ 3
(b)
A simple magnetic structure, similar to those examined in the previous examples, finds
common application in the so-calledvariable-reluctance position sensor, which, in turn, finds
widespread application in a variety of configurations for the measurement of linear and angular
position and velocity.
Formagnetic circuits with ac excitation, the concepts of inductance and energy storage come
into play along withFaraday’s lawof induction. Those concepts have been presented in some
detail in Section 1.2. The reader is encouraged to review that section, as that background will be
helpful in solving some of the problems related to this section.
11.3 Transformer Equivalent Circuits
It would be appropriate for the reader to review the material on transformers in Section 1.2.
Transformers come in various sizes, from very small, weighing only a few ounces, to very
large, weighing hundreds of tons. The ratings of transformers cover a very wide range. Whereas
transformers applied with electronic circuits and systems usually have ratings of 300 VA or less,
power-system transformers used in transmission and distribution systems have the highest volt-
ampere ratings (a few kVA to several MVA) as well as the highest continuous voltage ratings.
Instrument transformers (potential transformers and current transformers) with very small volt-
ampere ratings are used in instruments for sensing voltages or currents in power systems.
