# Electric Drives Questions and Answers – Induction Motors – Controlling Speed by Adjusting the Stator Voltage

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This set of Electric Drives Problems focuses on “Induction Motors – Controlling Speed by Adjusting the Stator Voltage”.

1. The stator voltage control method is a part of the slip changing technique.
a) True
b) False

Explanation: Stator voltage control method comes under slip changing technique. The load torque remains constant here. SV2=constant.

2. Calculate the value of new slip using the given data: V1=12 V, S1=.1, V2=5.
a) 0.576
b) 0.247
c) 0.487
d) 0.987

Explanation: This question is based on the concept of stator voltage control method. The load torque remains constant. S1V12=S2V22=constant. S2=.576.

3. Calculate the average value of the sinusoidal waveform y(t)=4.56cos(77.64πt+4800π÷68).
a) 41 V
b) 0 V
c) 48 V
d) 78 V

Explanation: Sinusoidal waveform is generally expressed in the form of V=Vmsin(ωt+α) where Vm represents peak value, ω represents angular frequency, α represents a phase difference. The average value of a sine wave is zero because of equal and opposite lobes areas. Since sine wave is an odd function then the net area of the waveform over a period is Net area = A+(-A) = 0. The average value is Net area÷Time=0.

4. R.M.S value of the periodic square waveform of amplitude 20 V is _______
a) 20 V
b) 18 V
c) 17 V
d) 13 V

Explanation: R.M.S value of the periodic square waveform is Vm and r.m.s value of the trapezoidal waveform is Vm÷3½. The peak value of the periodic square waveform is Vm. Vm=20 V.

5. Calculate the time period of the waveform y(t)=sin(.1πt)+cos(.2πt).
a) 20 sec
b) 30 sec
c) 40 sec
d) 10 sec

Explanation: The fundamental time period of the sine and cosine wave is 2π. The time period of y(t) is L.C.M {20,10}=20 sec. The time period is independent of phase shifting and time shifting.

6. The V/F control is a part of the synchronous speed changing technique.
a) True
b) False

Explanation: V/F control comes under the synchronous speed changing technique. Speed above or below synchronous speed can be achieved using V/F control.

7. The slope of the V-I curve is 56.489°. Calculate the value of resistance. Assume the relationship between voltage and current is a straight line.
a) 1.5 Ω
b) 1.6 Ω
c) 2.5 Ω
d) 1.4 Ω

Explanation: The slope of the V-I curve is resistance. The slope given is 56.489° so R=tan(56.489°)=1.5 Ω. The slope of the I-V curve is reciprocal of resistance.

8. If induction motor air gap power is 28.63 KW and gross developed power is 18.8 KW, then rotor ohmic loss will be _________ KW.
a) 9.83
b) 10.55
c) 15.54
d) 4.74

Explanation: 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=28.63-18.8=9.83 KW.

9. Calculate the value of inductive reactance if F=50 Hz and L=12 H.
a) 3768 Ω
b) 2578 Ω
c) 2477 Ω
d) 2456 Ω

Explanation: Inductive reactance can be calculated using the relation XL=2×3.14×f×L. The value of inductive reactance is XL=2×3.14×50×12=3768 Ω.

10. Calculate the value of capacitive reactance if F=60 Hz and C=14 H.
a) 189.5 mΩ
b) 252.4 mΩ
c) 244.5 mΩ
d) 244.8 mΩ

Explanation: Capacitive reactance can be calculated using the relation Xc=1÷2×3.14×f×L. The value of capacitive reactance is Xc=1÷2×3.14×50×12=189.5 mΩ.

11. Calculate the time period of the waveform v(t)=.6sin(.1πt+8π)+17cos(2πt+π)+ 4tan(.1πt).
a) 88 sec
b) 20 sec
c) 70 sec
d) 43 sec

Explanation: The fundamental time period of the sine wave is 2π. The time period of v(t) is L.C.M {20,1,20}=20 sec. The time period is independent of phase shifting and time shifting.

12. Calculate the value of resistance if total heat dissipated is 78 W when 5 A current flows through it.
a) 3.12 Ω
b) 2.24 Ω
c) 1.45 Ω
d) 5.13 Ω

Explanation: The resistor is a linear element. It only absorbs real power and dissipates it in the form of heat. The voltage and current are in the same phase in case of the resistor so the angle between V & I is 0°. R=P÷I2=3.12 Ω.

13. The value of slip at the starting of an induction motor is ________
a) 0
b) 1
c) 2
d) 3

Explanation: The maximum torque occurs when the slip value is equal to R2÷X2. At the starting, the rotor speed is equal to zero so slip value is 1.

14. The value of the slip of an induction motor during full load condition is ________
a) 0.99
b) .1
c) .8
d) 0 