1. A 32-pole, 3-phase, 70 Hz induction motor is operating at a speed of 112 rpm. The frequency of the rotor current of the motor in Hz is __________
A. 40.2
B. 46.1
C. 40.1
D. 40.6
Answer: C
Given a number of poles = 32.
Supply frequency is 70 Hz.
Rotor speed is 112 rpm.
Ns = 120×f÷P
=120×70÷32 = 262.5 rpm.
S=Ns-Nr÷Ns
= 262.5-112÷262.5=.573.
F2=sf=.573×70=40.1 Hz.
2. A 20-pole, 3-phase, 90 Hz induction motor is operating at a speed of _______ rpm. The frequency of the rotor current of the motor in Hz is 20.
A. 418.56
B. 420.12
C. 421.23
D. 422.45
Answer: B
Given a number of poles = 20.
The supply frequency is 90 Hz.
Ns=120×f÷P
=120×90÷20 = 540 rpm.
S=20÷90 = .222 Hz.
Nr=(1-s)Ns = 420.12 rpm.
Rotor speed is 420.12 rpm.
3. Calculate the amplitude of the sinusoidal waveform z(t)=.27sin(.369πt+.142π÷4.25).
A. .287
B. .270
C. .216
D. .287
Answer: B
The sinusoidal waveform is generally expressed in the form of
V=Vmsin(ωt+α)
where
Vm represents the peak value
ω represents the angular frequency
α represents a phase difference.
By comparing the waveform z(t) with the generalized sinusoidal expression we can see
Vm=.27 and ω=.369π rad/s.
4. R.M.S value of the sinusoidal waveform q(t)=2.11cos(87.25t+78π÷478.23).
A. 1.49 V
B. 1.56 V
C. 1.12 V
D. 1.78 V
Answer: A
R.M.S value of the sinusoidal waveform is Vm÷2½ and r.m.s value of the trapezoidal waveform is Vm÷3½.
The peak value of the sinusoidal waveform is Vm. The r.m.s value is
Vrms = 2.11÷2½ = 1.49 V.
5. The no-load circuit test on a 3-Φ induction motor is conducted at a rotor speed of _______
A. Zero
B. < Ns
C. > Ns
D. Ns
Answer: D
A no-load circuit test in an induction motor is also called an open circuit test so it is conducted at synchronous speed. Net input power taken is equal to the no-load rotational losses.
6. If induction motor air gap power is 67 KW and mechanically developed power is 26 KW, then rotor ohmic loss will be _________ KW.
A. 41
B. 42
C. 43
D. 44
Answer: A
Rotor ohmic losses are due to the resistance of armature windings. Net input power to the rotor is equal to the sum of rotor ohmic losses and mechanically developed power.
Rotor ohmic losses=Air gap power-Mechanical developed power
=67-26=41 KW.
7. Calculate the line voltage in the star connection when phase voltage=45 V.
A. 77.9 V
B. 77.6 V
C. 77.2 V
D. 77.8 V
Answer: A
The line voltage in the case of star connection is 1.73 times of phase voltage. It leads the phase voltage by an angle of 30°.
VL-L=1.73×45=77.9 V.
8. The slope of the V-I curve is 1.1°. Calculate the value of resistance. Assume the relationship between voltage and current is a straight line.
A. .019 Ω
B. .036 Ω
C. .075 Ω
D. .084 Ω
Answer: A
The slope of the V-I curve is resistance.
The slope given is 1.° so R=tan(1.1°)=.019 Ω.
The slope of the I-V curve is reciprocal to resistance.
9. If induction motor rotor power is 157.5 KW and gross developed power is 79.9 KW, then rotor ohmic loss will be _________ KW.
A. 77.5
B. 77.6
C. 76.9
D. 77.1
Answer: B
Rotor ohmic losses are due to the resistance of armature windings. Net input power to the rotor is equal to the sum of rotor ohmic losses and mechanically developed power.
Rotor ohmic losses=Air gap power-Mechanical developed power
=157.5-79.9=77.6 KW.
10. The power factor of a squirrel cage induction motor generally is ___________
A. .6-.8
B. .1-.2
C. .2-.4
D. .5-.7
Answer: A
At light loads, the current drawn is largely a magnetizing current due to the air gap and hence the power factor is low. The power factor of a squirrel cage induction motor generally is .6-.8.
