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EXERCISE 1
EMT 113 - ELECTRICAL ENGINEERING TECHNOLOGY
1. The armature winding of a dc motor has 320 conductors, only 70 % of which
lie directly under the poles, where the flux density B = 1.1 T. The armature
diameter is 26 cm and its length is 18 cm. the conductor current is 12 A.
Determine:
a) The total force created by the conductor.
b) The torque developed.
(532 N, 69.2 N.m)
2. The armature of a 120V dc motor has a resistance of 1.5 Ω and takes 4A when
operating at full load. Calculate:
a) The counter EMF produced by the armature.
b) The power developed by the armature.
c) Calculate the speed of the motor if the armature winding of the four poles
dc motor has 360 conductors and 0.01 Wb flux per pole.
(114V; 456W;950 r/min)
3. A shunt generator has a field resistance of 60 Ω. When the generator delivers
60kW the terminal voltage is 120 V, while the generated EMF is 133 V.
Determine:
a) The armature circuit resistance
b) The generated EMF when the output is 20kW and the terminal voltage is
135 V.
(0.25Ω; 139.3 V)
4. The magnetization curve for a separately excited dc generator is shown in
Figure 1. The generator is rated at 6 kW, 120 V, 50 A, and 1800 r/min and is
shown in Figure 2. Its field circuit is rated at 5 A. The following data are
known about the machine:
RA= 0.18 Ω
VF= 120 V
Radj= 0 to 30 Ω RF=24 Ω
NF= 1000 turns per pole
Answer the following questions about this generator, assuming that no
armature reaction.
(a) If this generator is operating at no load, what is the range of voltage
adjustments that can be achieved by changing Radj?
(b) If the field rheostat is allowed to vary from 0 to 30 Ω and the generator’s
speed is allowed to vary from 1500 to 2000 r/min, what are the
maximum and minimum no-load voltages in the generator?
(129 V, 87.4 V, 143 V, 72.8 V)
Figure 1: The magnetization curve for Question 4. This curve was taken at a speed 1800
r/min.
Figure 2: The separately excited dc generator.
5. At a location in Europe, it is necessary to supply 300 kW of 60 Hz power. The
only power sources available operate at 50 Hz. It is decided to generate the
power by means of a motor-generator set of a synchronous motor driving a
synchronous generator. How many poles should each of the two machines
have in order to convert 50 Hz to 60 Hz power?
(Pmotor = 10, Pgenerator = 12)
6. A 13.8 kV 10 MVA 0.8 PF lagging 60 Hz two-pole Y-connected steamturbine generator has a synchronous reactance of 12  per phase and
armature resistance of 1.5  per phase.
(a) What is the magnitude of EA at rated conditions?
(EA = 12040 V)
(b) What is the torque angle of the generator at rated conditions?
(Torque angle = 17.6)
(c) If the field current is constant, what is the maximum power possible
out of this generator?
(PMAX = 24.0 MW)
(d) At the absolute maximum power possible, how much reactive power
will this generator be supplying or consuming? Sketch the
corresponding phasor diagram.
7. A 480 V 60 Hz, four-pole synchronous motor draws 50 A from the line at
unity power factor and full load. Assuming that the motor is lossless:
(a) What is the output torque of this motor?
(Output torque = 221 Nm)
(b) What must be done to change the power factor to 0.8 leading? Explain
your answer using phasor diagrams.
(c) What will the magnitude of the line current be if the power factor is
adjusted to 0.8 leading?
(IL = 62.5 A)
8. A 480 V 100 kW 0.85 PF leading 50 Hz six pole Y-connected synchronous
motor has a synchronous reactance of 1.5  and a negligible armature
resistance. The rotational losses are also to be ignored. This motor is to be
operated over a continuous range of speeds from 300 to 1000 r/min, where the
speed changes are to be accomplished by controlling the system frequency
with solid-state drive.
(a) Over what range must the input frequency be varied to provide this
speed control range?
(15 Hz – 50 Hz)
(b) How large is EA at the motor’s rated conditions?
(EA = 429 V)
(c) What is the maximum power the motor can produce at the rated
conditions?
(PMAX = 238 kW)
(d) What is the largest EA could be at 300 r/min?
(EA = 129 V)
(e) Assuming that the applied voltage V is derated by the same amount as
EA, what is the maximum power the motor could supply at 300 r/min?
(PMAX = 238 kW)
(f) How does the capability of a synchronous motor relate to its speed?
9. A three-phase, 60 Hz induction motor runs at 890 r/min at no load and at 840
r/min at full load.
(a) How many poles does this motor have?
(P = 8)
(b) What is the slip at the rated load?
(s = 6.67%)
(c) What is the speed at one-quarter of the rated load?
(0.0167)
(d) What is the rotor’s electrical frequency at one-quarter of the rated
load?
(1 Hz)
10. A three-phase, 60 Hz, four pole induction motor runs at a no-load speed of
1790 r/min and a full load speed of 1720 r/min.
(a) Calculate the slip and the electrical frequency of the rotor at no load
and full-load conditions.
(0.33 Hz, 2.67 Hz)
(b) What is the speed regulation of this motor?
( 4.1%)
11. A 208 V, two-pole, 60 Hz Y-connected wound-rotor induction motor is rated
at 15 hp. Its equivalent circuit components are:
R1 = 0.20 
R1 = 0.12 
Pmech = 250 W
XM = 15.0  X1 = 0.41  X2 = 0.41 
Pmisc = 0 W
Pcore = 180 W
For a slip of 0.05, find
(a) The line current IL
( 44.8 -25.5 A))
(b) The stator copper losses PSCL
( 1205 W)
(c) The air gap power PAG
( 13.4 kW)
(d) The power converted from electrical to mechanical form Pconv
( 12.73 kW)
(e) The induced torque  ind
( 35.5 Nm)
(f) The load torque  load
( 34.3 Nm)
(g) The overall machine efficiency
( 84.5 %)
(h) The motor speed
( 3420 r/min)