Faculty of Electrical Engineering
Electric Machines & Drives ELCT 403
Dr. Eng. Noha Shouman
Eng. Omar Salah
Tutorial (2)
Magnetic Circuits
Problem 1
Coils A and B have mutual inductance 25 mH. At time t = 0 the current in coil A is zero. Subsequently a
time-varying current is supplied to A. Find an expression for the time-varying current in coil A if the
induced emf in coil B is given by the following equation
𝐸𝐵 = (50 + 0.2𝑡) 𝑉/𝑚𝑠
Problem 2
Consider the magnetic core with an air gap as shown in Figure 1. The core material has a relative
permeability of 6000 and a rectangular cross-section of 2cm by 3cm. The coil has 500 turns. Assume that
fringing in the air gap increases the effective cross-sectional area of the air gap by 5 percent. Determine the
current required to establish a flux density of Bgap=0.25 T in the air gap. (Hint: consider the mean length of
the air gap)
Figure 1
Problem 3
A ferromagnetic core is shown in Figure 2. The depth of the core is 5 cm. The other dimensions of the core are
as shown in Figure 2.
a) Draw the equivalent magnetic circuit of Figure 2.
b) Find the value of the current that will produce a flux of 0.005 Wb?
c) With this current, find the flux density at the top of the core? What is the flux density at the right side
of the core? (Assume that the relative permeability of the core is 1000.)
Figure 2
Faculty of Electrical Engineering
Electric Machines & Drives ELCT 403
Dr. Eng. Noha Shouman
Eng. Omar Salah
Problem 4
A two-legged core is shown in Figure 3. The winding on the left leg of the core (N1) has 400 turns, and the
winding on the right (N2) has 300 turns. The coils are wound in the directions shown in the Figure 3. If the
dimensions are as shown, then what flux would be produced by currents i1 = 0.5 A and i2 = 0.75 A?
(Assume µr = 1000 and constant.)
(
Figure 3
Problem 5
Figure 4 shows the core of a simple DC motor. The magnetic flux density is 1.2 T while the relative
permeability of the core (stator and rotor) is 3800. Assume that the cross-sectional area of each air gap is 18
cm2 and that the width of each air gap is 0.05 cm. The effective diameter of the rotor core is 4 cm.
a) Draw the magnetic circuit of Figure 4.
b) Find the number of turns if the current inside the coil is 1 A.
Figure 4
Faculty of Electrical Engineering
Electric Machines & Drives ELCT 403
Dr. Eng. Noha Shouman
Eng. Omar Salah
Problem 6
The magnetic circuit shown in Figure 5 has two windings and two air gaps. The core can be assumed to be
of infinite permeability. Derive an expression for the self-inductances of windings 1 and 2 and the mutual
inductance between the windings.
Figure 5
Problem 7
A system of three coils on an ideal core is shown in Figure 6 where the number of turns of each coil and the
airgap lengths are given in the following table.
N1 N2 N3 g1 g2 g3
500 turns 250 turns 500 turns 4 mm 2 mm 2 mm
If the cross-sectional area was constant throughout the core, which is equal to 100 mm2, calculate:
a) The self-inductance of coil N1.
b) The mutual inductance between coils N2 and N3.
Figure 6
