Fayoum University
Faculty of Engineering
Electrical Engineering Department
AC Machines Course
rd
3 year, Electrical Power & Machines Branch
Sheet 1 – Magnetic Circuits
Problem 1-1: In the magnetic system of the following figure. Two
sides are thicker than other two sides. The depth of the core is 10 cm,
the relative permeability of the core 𝝁𝒓 = 2000 , the number of turns
N=300, the current flowing through the coil is i = 1A.
a) Determine flux in the core
b) Determine flux density in the parts of the core
Problem 1-2: A ferromagnetic core with a relative permeability of
1500 is shown in the following Figure. The dimensions are as shown
in the diagram, and the depth of the core is 5 cm.
The air gaps on the left and right sides of the core are 0.050 and 0.070
cm, respectively.
Because of fringing effects, the effective area of the air gaps is 5
percent larger than their physical size.
If there are 300 turns in the coil wrapped around the center leg of the
core and if the current in the coil is 1.0 A, then:
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Eng. Ahmad Yasser Ahmad
Fayoum University
Faculty of Engineering
Electrical Engineering Department
AC Machines Course
rd
3 year, Electrical Power & Machines Branch
a) What is the flux in each of the left, center, and right legs of the
core?
b) What is the flux density in each air gap?
Problem 1-3: The toroidal core (Donut shaped) shown in following
figure is made from some material with relative permeability of 3000.
It has current of 5 Amps passing through its coil.
Calculate:
i.
ii.
iii.
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Reluctance of the core.
Core flux and flux linkage 𝝀
Flux density through the core
Eng. Ahmad Yasser Ahmad
Fayoum University
Faculty of Engineering
Electrical Engineering Department
AC Machines Course
rd
3 year, Electrical Power & Machines Branch
Problem 1-4: A wire is shown in the following Figure which is
carrying 2.0 A in the presence of a magnetic field.
Calculate the magnitude and direction of the force induced on the
wire.
Problem 1-5: The wire is shown in the following Figure is moving in
the presence of a magnetic field. With the information given in the
figure: Determine the magnitude and direction of the induced
voltage in the wire.
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Eng. Ahmad Yasser Ahmad
Fayoum University
Faculty of Engineering
Electrical Engineering Department
AC Machines Course
rd
3 year, Electrical Power & Machines Branch
Problem 1-6: The symmetric magnetic circuit of Figure has three
windings. Windings A and B each have N turns and are wound on the
two bottom legs of the core. The core dimensions are indicated in the
figure.
a. Find the self-inductances of each of the windings.
b. Find the mutual inductances between the three pairs of
windings.
c. Find the voltage induced in winding I by time-varying currents
iA (t) and iB (t) in windings A and B. Show that this voltage can be
used to measure the imbalance between two sinusoidal currents of
the same frequency.
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Eng. Ahmad Yasser Ahmad
Fayoum University
Faculty of Engineering
Electrical Engineering Department
AC Machines Course
rd
3 year, Electrical Power & Machines Branch
Home Task-1: The magnetic circuit of Figure has two windings and
two air gaps. The core can be assumed to be of infinite permeability.
The core dimensions are indicated in the figure.
a. Assuming coil 1 to be carrying a current I1 and the current in
coil 2 to be zero,
Calculate:
i. the magnetic flux density in each of the air gaps
ii. the flux linkage of winding l
iii. The flux linkage of winding 2.
b. Repeat part (a), assuming zero current in winding 1 and a
current I2 in winding 2.
c. Repeat part (a), assuming the current in winding 1 to be I1 and
the current in winding 2 to be I2.
d. Find the self-inductances of windings 1 and 2 and the mutual
inductance between the windings.
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Eng. Ahmad Yasser Ahmad