University of Tehran
Electrical Machines I
Homework 1 (Principals)
Due: Next Sunday
1- Consider the following two coils. Explain that what
changes may influence the Self and Mutual Inductances
between these coils. If you can, derive a formula for the
Self and Mutual Inductances of this system according to
its variables.
2-
A ferromagnetic core with a relative permeability of 1500 is shown below. The dimensions are as
shown in the diagram, and the depth of the core is 7cm. The air gaps on the left and right sides of the
core are 0.07 and 0.02cm, respectively. Because of fringing effects, the effective area of the air gaps is
%5 larger than their physical size. If there are 400 turns in the coil wrapped around the center leg of
the core and if the current in the coil is 1A, what is the flux in each of the left, center, and right legs of
the core? What is the flux density in each air gap?
3- A core with three legs is shown in the following. Its depth is 8 cm, and there are 400 turns on the
center leg. The remaining dimensions are shown in the figure. The core is composed of a steel having
the magnetization curve shown in the next figure. Answer the following questions about this core:
(a) What current is required to produce a flux density of 0.5T in the central leg of the core?
(b) What current is required to produce a flux density of 1T in the central leg of the core? Is it twice
the current in part (a)?
(c) What are the reluctances of the central and right legs of the core under the conditions in part (a)?
(d) What are the reluctances of the central and right legs of the core under the conditions in part (b)?
(e) What conclusion can you make about
reluctances in real magnetic cores?
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University of Tehran
Electrical Machines I
Homework 1 (Principals)
Due: Next Sunday
4- The core shown in the following has the flux Φ shown in the next Figure. Sketch the voltage present at
the terminals of the coil.
5- The magnetic circuit below has the following
dimensions:
2
University of Tehran
Electrical Machines I
Homework 1 (Principals)
Due: Next Sunday
Project1 (Bonus)
Please consider that your articles should be in the proper format (IEEE format).
Besides, you should present your work or research in the class. Don’t copy the
other’s work or paper, just use them as your references and then write your own. The
simulations can be done by any software such as MATLAB, PSPICE, PSCAD, ATP
(EMTP), COMSOL, MAXWELL (FEM), ANSIS and so on. Remember the
notifications that we discussed in the first class.
Subjects:
1- What are Additional Losses in the Ferrite cores (beside of the hysteresis and
eddy current losses)?
2- Methods for reducing the losses in the ferrite cores
3- How we can model the fringing effect on the edges of the air gaps?
Good Luck
H.A
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