1. A dc test is performed on a 460-V, A-connected, 100-hp induction motor. 7.

A 208-V, two-pole, 60-Hz, Y-connected wound-rotor induction motor is

If VDC = 24 V and IDC = 80 A, what is the stator resistance R₁? Why is this so? rated at 15 hp. Its equivalent circuit components are
2. A 220-V, three-phase, two-pole, 50-Hz induction motor is running at a slip R₁ = 0.200 Ω R2 = 0.120 Ω Хм = 15.0 Ω Χ₁ = 0.410 Ω Χ2 = 0.410 Ω
of 5 per- cent. Find: Pmech = 250 W Pmisc = 0 Pcore = 180 W & for a slip of 0.05
(a) The speed of the magnetic fields in revolutions per minute i)what is the pullout torque?
(b) The speed of the rotor in revolutions per minute ii)What is the slip at the pullout torque?
(c) The slip speed of the rotor iii)What is the rotor speed at the pullout torque?
(d) The rotor frequency in hertz iv)If the motor is to be driven from a 440-V, 60-Hz power supply, what will
3. A three-phase, 60-Hz induction motor runs at 890 r/min at no load and at the pullout torque be? What will the slip be at pullout?
840 r/min at full load. 8.A 208-V,60 Hz,6-pole, Y-connected, 25-hp design class B induction motor is
(a) How many poles does this motor have? tested in the laboratory, with the following results:
(b) What is the slip at rated load? No load: 208 V, 22.0 A, 1200 W, 60 Hz
(c) What is the speed at one-quarter of the rated load? Locked rotor: 24.6 V, 64.5 A, 2200 W, 15 Hz
(d) What is the rotor's electrical frequency at one-quarter of the rated load? DC test: 13.5 V, 64 A
4. A 50-kW, 440-V, 50-Hz, six-pole induction motor has a slip of 6 percent Find the equivalent circuit of this motor.
when operating at full-load conditions. At full-load conditions, the friction 9.A 460-V, four-pole, 50-hp, 60-Hz, Y-connected, three-phase induction
and windage losses are 300 W, and the core losses are 600 W. Find the motor develops its full-load induced torque at 3.8 percent slip when
following values for full- load conditions: operating at 60 Hz and 460V. The per-phase circuit model impedances of the
(a) The shaft speed n motor are
(b) The output power in watts R₁ = 0.33 Ω ΧΜ = 30 Ω M Χ₁ = 0.42 Ω Χ2 = 0.42 Ω
(c) The load torque Toad in newton-meters Mechanical, core, and stray losses may be neglected in this problem.
(d) The induced torque Tind in newton-meters (a) Find the value of the rotor resistance R2.
(e) The rotor frequency in hertz (b) Find Tmax, Smax, and the rotor speed at maximum torque for this motor.
5. A three-phase, 60-Hz, four-pole induction motor runs at a no-load speed (c) Find the starting torque of this motor.
of 1790 r/min and a full-load speed of 1720 r/min. Calculate the slip and the (d) What code letter factor should be assigned to this motor?
electrical frequency of the rotor at no-load and full-load conditions. What is (e) If this motor is started from a 460-V infinite bus, how much current will
the speed regulation of this motor flow in the motor at starting?
6. A 208-V, two-pole, 60-Hz, Y-connected wound-rotor induction motor is (f) If transmission line with an impedance of 0.35 + 10.25 2 per phase is used
rated at 15 hp. Its equivalent circuit components are to connect the induction motor to the infinite bus, what will the starting
R₁ = 0.200 Ω R2 = 0.120 Ω Хм = 15.0 Ω Χ₁ = 0.410 Ω Χ2 = 0.410 Ω current of the motor be? What will the motor's terminal voltage be on
Pmech = 250 W Pmisc = 0 Pcore = 180 W ,For a slip of 0.05, find starting?
(a) The line current IL (b) The stator copper losses PSCL (g) If an ideal 1.4:1 step-down autotransformer is connected between the
(c) The air-gap power PAG transmission line and the motor, what will the current be in the transmission
(d) The power converted from electrical to mechanical form Pconv line during starting? What will the voltage be at the motor end of the
(e) The induced torque Tind (f) The load torque Tload transmission line during starting?
(g) The overall machine efficiency
(h) The motor speed in revolutions per minute and radians per second
10.[viva basic] 13.When it is necessary to stop an induction motor very rapidly, many
In this chapter, we learned that a step-down autotransformer could be used induction motor controllers reverse the direction of rotation of the magnetic
to reduce the starting current drawn by an induction motor. While this fields by switching any two stator leads. When the direction of rotation of
technique works, an autotransformer is relatively expensive. A much less the magnetic fields is reversed, the motor develops an induced torque
expensive way to reduce the starting current is to use a device called Y-A opposite to the current direction of rotation, so it quickly stops and tries to
starter. If an induction motor is normally A-connected, it is possible to start turning in the opposite direction. If power is removed from the stator
reduce its phase voltage V (and hence its starting cur- rent) by simply circuit at the moment when the rotor speed goes through zero,then the
reconnecting the stator windings in Y during starting, and then restoring the motor has been stopped very rapidly. This technique for rapidly stopping an
connections to A when the motor comes up to speed. Answer the following induction motor is called plugging. A 460-V, four-pole, 50-hp, 60-Hz, Y-
questions about this type of starter. connected, three-phase induction motor develops its full-load induced
(a) How would the phase voltage at starting compare with the phase voltage torque at 3.8 percent slip when operating at 60 Hz and 460V with The per-
under normal running conditions? phase circuit model impedances of the motor given as
(b) How would the starting current of the Y-connected motor compare to R₁ = 0.33 Ω ΧΜ = 30 Ω M Χ₁ = 0.42 Ω Χ2 = 0.42 Ω is running at rated
the starting current if the motor remained in a A-connection during starting? conditions and is to be stopped by plugging.
11.A 460-V, 100-hp, four-pole, A-connected, 60-Hz, three-phase induction (a) What is the slip s before plugging?
motor has a full-load slip of 5 percent, an efficiency of 92 percent, and a (b) What is the frequency of the rotor before plugging?
power factor of 0.87 lagging. At start-up, the motor develops 1.9 times the (c) What is the induced torque Tind before plugging?
full-load torque but draws 7.5 times the rated current at the rated voltage. (d) What is the slip s immediately after switching the stator leads?
This motor is to be started with an auto- transformer reduced-voltage (e) What is the frequency of the rotor immediately after switching the stator
starter. leads?
(a) What should the output voltage of the starter circuit be to reduce the (f) What is the induced torque Tind immediately after switching the stator
starting torque until it equals the rated torque of the motor? leads?
(b) What will the motor starting current and the current drawn from the
supply be at this voltage?
12.A wound-rotor induction motor is operating at rated voltage and
frequency with its slip rings shorted and with a load of about 25 percent of
the rated value for the ma- chine. If the rotor resistance of this machine is
doubled by inserting external resistors into the rotor circuit, explain what
happens to the following:
(a) Slip s (b) Motor speed nm (c) The induced voltage in the rotor
(d) The rotor current (e) Tind (f) Pout (g) PRCL (h) Overall efficiency η
13.Answer the following questions about a 460-V, A-connected, two-pole,
75-hp, 60-Hz, starting-code-letter-E induction motor:
(a) What is the maximum current starting current that this machine's
controller must be designed to handle?
(b) If the controller is designed to switch the stator windings from a A
connection to a Y connection during starting, what is the maximum starting
current that the controller must be designed to handle?
(c) If a 1.25:1 step-down autotransformer starter is used during starting,
what is the maximum starting current that will be drawn from the line?