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ECET 3500 Spring 2005 Electric Machines Sample Exam I ECET 3500 Spring 2005
Electric Machines Sample Exam I

.

Instructions: Show all of your work, making sure your work in legible and that your reasoning can be
followed. No credit will be given for illegible or illogical work, or for final answers that are not justified
by the work show. Place all final answers in the spaces provided. This exam is closed book, except for
one 4x6 note-card which may contain no solved problems.

Problem #1) Determine the effective length of a conductor required to generate 10 volts when passing through and normal
(
) to a magnetic field of 1.0 Tesla at a speed of 10 m/sec. Given the same conductor exposed to the same
magnetic field, if a DC current of 250mA is applied to the conductor, determine the magnitude of the force
created on the conductor. Note that you will need to use your calculated length to solve the second part of
this problem.








l
eff
= _____________1________________m


F
=
____________0.25______________Nm

Problem #2) A 150-turn coil is wound around a ferromagnetic core having an average core length of 25 cm. The
magnetization curve for the core material is shown below. A current of 0.5 amps flows through the coil.
Determine the mmf created by the coil, the magnetic field intensity within the core, and the relative
permeability of the core under these conditions.













mmf
=
__________75_______________At


H
=
____________300____________At/m









�
r
= _____________1724_______________

Problem #3) A conductor carrying a current is sitting within a uniform magnetic field, as shown in the figure below.
Determine the direction of the force upon the conductor and briefly explain the reasoning behind your
answer in the space below. Draw an arrow on the figure below to specify your chosen direction.



Downward - see text for theory



Problem #4) Define eddy currents with respect to transformers including what they are and why they are created.

See text

Problem #5) The following short-circuit test data was obtained for a 50 KVA, 2400600V, 60 Hz transformer:
V
SC
= 76.4 V, I
SC
= 20.8 A, P
SC
= 954 W
Determine
the
series equivalent impedance of the transformer referred to the high voltage side, and the
series equivalent percent impedance.










Z
eqHS
= ______2.2+j2.94____________











Z
eq%
= _______1.914+j2.55 %________
.
M
N
I
H (At/m)
B (Wb)
10
100
1k
10k
32
320
3.2k
32k
0.2
0.4
0.6
0.8
1.0 Problem #6) A core-type transformer rated at 30 KVA, 2400 480 V, and 60 Hz has a core whose mean length is 0.85
meters and whose cross-sectional area is 80 cm
2
. Rated voltage at no-load produces a magnetic field
intensity of 352 At/m and a maximum flux density of 1.5 Tesla within the core. Determine the number of
turns in both the high and the low voltage windings, and the magnitude of the current that will be drawn
into the high-voltage winding while the low-voltage winding is open-circuited if rated voltage is applied.













N
HS
= ___________750____________turns










N
LS
= ___________150____________turns










|I
HV(noload)
| = _______0.4___________amp



Problem #7) Determine the source voltage and current (in phasor form) in the following circuit that contains an ideal iron-
core transformer. Also, determine the value of an impedance that could be used to model the input
impedance or the transformer with the specified loads connected to the secondary winding.










V
source
= _________56.57<-45�________V










I
source
= __________0.354<-45�_______ A










Z
in
= ____________160+j0__________


Problem #8) Given a 3 KVA, 60 Hz, 2400600 V transformer with the following winding and excitation impedances:
Windings: R
HS
= 2.6
, X
HS
= 2.8
, R
LS
= 0.15
, X
LS
= 0.2

Excitation: R
fe(HS)
= 1600
, X
M(HS)
= 600


If the transformer is used to connect a 2400
0� volt source to a load of Z
Load
= 20
, determine the actual
load voltage (in polar form) and the real power supplied to the load.









V
Load
= __________590<-1�______________volts








P
Load
= ___________17444_______________watts

Problem #9) For each of the following, specify whether or not each of the responses is true or false.

___<b>T
RUE
___ The Magneto-Motive Force (MMF) created by a source coil in a magnetic circuit is proportional to the
current flowing in the coil.
___<b>F
ALSE
___ The voltage source in the laboratory has both a constant and a variable 220/110 volt three-phase supply.

___<b>T
RUE
___ The magnetization current in a transformer is the current required to create the no-load magnetic field in a
lossless magnetic core.
___<b>F
ALSE
___ The excitation current in a transformer is the current required to create the full-load magnetic field in the
magnetic core.
___<b>F
ALSE
___ The turns ratio of a transformer is specified by the ratio of the rated high-side voltage compared to the
rated low-side voltage.
___<b>F
ALSE
___ Eddy currents are circulating currents in the transformer core resulting from the time-varying current in
the load.
___<b>T
RUE
___ The magnitude of the currents in the primary and secondary coils of an ideal transformer will have the
inverse ratio of the voltages across the primary and secondary coils.
___<b>T
RUE
___ The Open-Circuit Test for a transformer is used to determine the excitation impedances in the transformer
model.
___<b>T
RUE
___ For a practical conductor in the air, the strength of the magnetic field formed around the conductor will
double if the current flowing through the conductor itself is doubled.
___<b>T
RUE
___ The permeability of a material at a specific operating point is defined by the ratio of the flux density in the
material compared to the magnetic field intensity in the material.
___<b>T
RUE
___ The relative permeability of a material is the ratio of the actual permeability of the material at a specific
operating point compared to the permeability of free-space (air).
___<b>F
ALSE
___ As a magnetic core becomes saturated, the cores permeability will increase.

___<b>T
RUE
___ Lenzs Law states that any induced effect will always oppose its source.
M
E
HV
~
E
LV
~
N
LV
N
HV
-j10
10+j10
a=4
V
source
20<0 V
I
source ECET 3500 Summer 2004
Electric Machines Exam I

Print Name (Last Name First):
_________________________

Problem #1) A core-type transformer rated at 50 KVA, 2400 480 V, and 60 Hz has a core whose mean length is 0.8
meters and whose cross-sectional area is 10cmx10cm. While at no-load, the application of rated voltage to
the transformer produces a maximum magnetic field intensity of 800 At/m and a maximum flux density of
1.6 Tesla within the core. Determine the number of turns in both windings, and the magnitude of the
magnetization current that will be drawn into the high-voltage winding with applied rated voltage while
the low-voltage winding is open-circuited. Also, determine the high-voltage side rated input current, and
the relative permeability of the core at the specified maximum field intensity value.













N
HS
= __________563____________turns










N
LS
= __________113_____________turns










I
HV(noload)
= ______1.14____________amps










I
HV(rated)
= _______20.83__________amps










�
r
= ____________1591________________



Problem #2) Determine the source voltage and current (in phasor form) in the following circuit that contains an ideal iron-
core transformer. Also, determine the real power consumed by the load impedance connected to the
secondary winding of the transformer.











source
V~
= ______111.8
161.6� _________V










source
I
~
= _______14.14
90� __________ A










load
P
= __________500____________W


Problem #3) Given a 30 KVA, 60 Hz, 2400600 V transformer with the following winding and excitation impedances:
Windings: R
HS
= 2.6
, X
HS
= 2.8
, R
LS
= 0.15
, X
LS
= 0.2

Excitation: R
fe(HS)
= 1600
, X
M(HS)
= 600


If the transformer is supplied by a 2400
0� volt source and a load of Z
Load
= 15
is connected to the
secondary winding, determine the actual input current to the transformer (in polar form), as well as the
rated input current.











input
I
~
=