PROBLEMS 543yxB
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rotationFigure P12.1.3Rotating conducting loop.(c) Calculate the average mechanical torque
needed to turn the coil and generate power
for the resistor. Identify the action of the
device as that of a motor or a generator.
12.1.5The machine of Problem 12.1.4 can be used as a
motor. Let the terminals of the coil be connected
to a voltage source of 1 kV rms. If the motor runs
at 1800 r/min and draws a current of 2 A, find the
torque supplied to the mechanical load.
12.1.6The 50-turn coil in the configuration of Figure
P12.1.3 is rotated at a constant speed of 300
r/min. The axis of rotation is perpendicular to
a uniform magnetic flux density of 0.1 T. The
loop has widthw=10 cm and lengthl=1m.
Compute:
(a) The maximum flux passing through the coil.
(b) The flux linkage as a function of time.
(c) The maximum instantaneous voltage in-
duced in the coil.
(d) The time-average value of the induced volt-
age.
(e) The induced voltage when the plane of the
coil is 30° from the vertical.*12.1.7A 100-turn coil in the configuration of Figure
P12.1.3 is rotated at a constant speed of 1200
r/min in a magnetic field. The rms induced volt-
age across the coil is 1 kV, and each turn has a
lengthl= 112 .5 cm and a widthw=10 cm.
Determine the required value of the flux density.
12.1.8A sectional view of a cylindrical iron-clad
plunger magnet is shown in Figure P12.1.8. The
small air gap between the sides of the plunger
and the iron shell is uniform and 0.25 mm long.
Neglect leakage and fringing, and consider the
iron to be infinitely permeable. The coil has 1000
turns and carries a direct current of 3 A. Compute
the pull on the plunger forg= 1 .25 cm.
12.1.9Figure E12.1.1 can also be considered as a simple
model of a magnetically operated relay that is
commonly used for the automatic control and
protection of electric equipment. Consider the
core and armature (shown as “Bar” in Figure
E12.1.1) of the relay to be constructed out of
infinitely permeable magnetic material. The core
has a circular cross section and is 1.25 cm in
diameter, while the armature has a rectangular
cross section. The armature is so supported that
the two air gaps are always equal and of uniform
length over their areas. A spring (not shown in
the figure), whose force opposes the magnetic
pull, restrains the motion of the armature. If the
operating coil has 1800 turns carrying a current
of 1 A, and the gaps are set at 0.125 cm each, find
the pull that must be exerted by the spring. You
may neglect leakage and fringing.
12.1.10The coil is placed so that its axis of revolution
is perpendicular to a uniform field, as shown in
Figure P12.1.10. If the flux per pole is 0.02 Wb,
and the coil, consisting of 2 turns, is revolving at
1800 r/min, compute the maximum value of the
voltage induced in the coil.
12.2.1An elementary two-pole, single-phase, synchro-
nous machine, as illustrated in Figure P12.2.1,
has a field winding on its rotor and an armature
winding on its stator, withNf=400 turns and
Na=50 turns, respectively. The uniform air gap
is of length 1 mm, while the armature diameter is
0.5 m, and the axial length of the machine is 1.5
m. The field winding carries a current of 1 A (dc)
and the rotor is driven at 3600 r/min. Determine:
(a) The frequency of the stator-induced voltage.
(b) The rms-induced voltage in the stator wind-
ing.