ECE 3614
HW # 5
1. A three phase, induction motor is supplied with power from a 60 Hz source. At full load the
motor speed is 1728 rpm, and no load speed approaches 1800 rpm. For full load condition,
calculate the following:
a. Number of poles.
b. Slip.
c. Frequency of the rotor voltages.
d. Speed of the rotor field with respect to the rotor.
e. Speed of the rotor field with respect to the stator.
f. Speed of the rotor field with respect to the stator field.
2. A three phase, 220 V, four pole, 60 Hz induction motor has the following parameters referenced
to the stator. The total rotational loss is 500 W and the slip is 5%.
R1 = 0.3 Ω; R2 = 0.2 Ω
X1 = 0.5 Ω; X2 = 0.5 Ω; Xm = 15 Ω
a.
b.
c.
d.
e.
Motor speed.
Input current.
Input power factor.
Shaft torque.
Efficiency.
3. A three phase, 20 hp, 440 V, 60 Hz, wye-connected induction motor, operating at rated
conditions, draws line current of 18 A. Readings from machine tests are provided in the table.
Voltage (V)
Current (A)
Power (W)
No Load
(at 60 Hz)
440
9
3750
Determine R1, R2, X1, X2, Xm, and Protational.
Blocked Rotor
(at 15 Hz)
62
24
1800
DC
25
34
4. A three phase, 25 hp, 440 V, 60 Hz, six pole induction motor is operating at a slip of 4%. The
core loss and f+w losses for the load are 250 W and 125 W, respectively. The motor is wye
connected with the following per-phase parameters. Calculate values.
a.
b.
c.
d.
e.
f.
R1 = 0.35 Ω; R2 = 0.4 Ω
X1 = 1.25 Ω; X2 = 1.50 Ω; Xm = 25 Ω
Line current and power factor.
Real and reactive power input.
Air-gap power.
Mechanical power and torque developed.
Shaft horsepower and torque.
Efficiency of the motor.
5. A three phase, 20 hp, 480 V, 60 Hz, six pole wound-rotor induction motor is operating at rated
conditions, running at 1164 rpm with the rotor rheostat shorted. The per-phase parameters are
provided. Determine the following:
R1 = 0.30 Ω; R2 = 0.40 Ω
X1 = 1.50 Ω; X2 = 2.00 Ω; Xm = 300 Ω
a. Slip at which maximum torque occurs.
b. Maximum torque.
c. Resistance to be inserted in the rotor circuit to operate the motor at rated torque and speed
of 1074 rpm.
6. A three phase, 25 hp, 440 V, 60 Hz, 1750 rpm, wound-rotor induction motor has the following
per-phase parameters. The motor is connected to a three-phase, 440 V, 60 Hz supply.
R1 = 0.20 Ω; R2 = 1.0 Ω
X1 = 0.15 Ω; X2 = 0.80 Ω; Xm = 30 Ω
a. Calculate the starting torque.
b. Determine the resistance of the rheostat in the rotor circuit such that the maximum torque
occurs at starting.
7. A single phase, ¼ hp, 110 V, 60 Hz, 1725 rpm, four pole capacitor-start induction motor has the
following per-phase parameters for the main winding. The core loss at 110 V is 25 W, friction
and windage loss is 20 W. The motor is connected to a 110 V, 60 Hz supply, running at a slip of
5%. Calculate values.
a.
b.
c.
d.
R1 = 2.5 Ω; R2 = 4.0 Ω
X1 = 3.5 Ω; X2 = 3.5 Ω; Xm = 50 Ω
Input current and power factor.
Input power.
Mechanical power and torque developed.
Efficiency of the motor.