# Electrical Machines Questions and Answers – Elementary Synchronous Machines

This set of Electrical Machines Multiple Choice Questions & Answers (MCQs) focuses on “Elementary Synchronous Machines”.

1. Consider a single phase synchronous machine of cylindrical rotor type. A single phase supply is given to the stator winding and a voltmeter is connected across rotor winding. For what value of θr, the voltmeter reads maximum?
a) 90°
b) 0°
c) 45°
d) 30°

Explanation: When θr=0, the flux linkages with the rotor are maximum, and this is indicated by a maximum voltmeter reading.

2. Consider a single phase synchronous machine of cylindrical rotor type. A single phase supply is given to the stator winding, and a voltmeter is connected across rotor winding. For what value of θr the voltmeter reads a zero?
a) 0°
b) 30°
c) 45°
d) 90°

Explanation: When θr=90°, the voltmeter reading is zero, because the stator winding axis is perpendicular to the rotor winding axis, and the mutual inductance Msr is zero.

3. Which of the following equation best represents the mutual inductance between stator and rotor in a single phase cylindrical rotor synchronous machine? (where θr= space angle between stator and rotor field axis)
a) Msr=0
b) Msr=Mmax
c) Msr=Mmaxcosθr
d) Msr=Mmaxsinθr

Explanation: In a single phase cylindrical rotor synchronous machine, the Msr is maximum, when θr=0, and is zero when θr=90° and cosine function represents it.

4. In a single phase cylindrical rotor synchronous machine, the torque Te tends to ____________ the space angle θr.
a) reduce
b) increase
c) maintain constant
d) all of the mentioned

Explanation: Wfld(is,irr)=1/2 is2Ls+1/2 ir2Lr+ isirMmaxcosθr
Torque, Te=∂Wfld(is,irr)/∂θr= -isirMmaxsinθr
Negative sign indicates that the torque Te tends to reduce angle θr.

5. The following torque expression: Te=-isirMmaxsinθr is applicable in a single phase cylindrical rotor synchronous machine when the rotor is __________
a) revolving
b) stationary
c) revolving or stationary
d) none of the mentioned

Explanation: The torque expression is applicable whether the rotor is revolving or stationary.
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6. In a two phase cylindrical rotor synchronous machine, the self inductances Lα, Lβ for phases α,β respectively are __________
a) constant and equal
b) constant and unequal
c) varying and equal
d) varying and unequal

Explanation: Constant and equal, as the reluctance offered to the fluxes produced by phase α and β winding doesn’t vary with rotor movement.

7. In a two phase cylindrical rotor synchronous machine, the mutual inductance Mαβ between α phase and β phase winding is __________
a) Mmax
b) 0
c) Mmin
d) any of the mentioned

Explanation: Since the axes of phase α and phase β windings are normal to each other and air gap is uniform, the mutual inductance Mαβ between α,β winding is zero.

8. In a two phase cylindrical rotor synchronous machine, torque Te is _____________
a) constant at some instant of time
b) changing at every instant of time
c) constant at every instant of time
d) changing at some instant of time

Explanation: Te = IfImMmaxsinδ
We can observe that it remains constant at every instant of time.

9. Which of the following equation represents the reluctance torque of a salient pole synchronous machine?
a) Te(av) = 1/4 Im2(Ld-Lq)sin2δ
b) Te(av) = 2 Im2(Ld-Lq)sinδcosδ
c) Te(av) = 1/8 Im2(Ld-Lq)
d) Te(av) = 1/8 Im2(Ld-Lq)sin2δ

Explanation: Te(av) = 1/8 Im2(Ld-Lq)sin2δ+1/2 IfImMmaxsinδ
If field current If is reduced to zero, the reluctance torque Te(av) = 1/8 Im2(Ld-Lq)sin2δ.

10. Which component of torque equation, Te(av) = 1/8 Im2(Ld-Lq)sin2δ+1/2 IfImMmaxsinδ represents the electromagnetic/interaction torque in single phase salient pole synchronous machine?
a) 1/2 IfImMmaxsinδ
b) 1/8 Im2(Ld-Lq)sin2δ
c) 1/8 Im2(Ld-Lq)sin2δ + 1/2 IfImMmaxsinδ
d) none of the mentioned

Explanation: The torque developed by the interaction of both stator and rotor magnetic fields is the electromagnetic/interaction torque.

11. An electromechanical energy conversion device has cylindrical stator but salient pole rotor. If δ is the angle between stator field and rotor field, the average torque developed is proportional to (A and B are constants) __________
a) Asinδ
b) Asin2δ
c) Asinδ+Bsin2δ
d) δ

Explanation: Te(av) = 1/8 Im2(Ld-Lq)sin2δ+1/2 IfImMmaxsinδ = Asinδ+Bsin2δ.

12. An electromechanical energy conversion device has cylindrical stator but salient pole rotor. Rotor is not excited. If δ is the angle between stator field and rotor long axis, then average torque developed is proportional to (A and B are constants).
a) Asinδ
b) Asin2δ
c) Asinδ + Bsin2δ
d) zero

Explanation: We know, Te = 1/8 Im2(Ld-Lq)sin2δ+1/2 IfImMmaxsinδ, rotor is not excited implies If=0, and thus Te = 1/8 Im2(Ld-Lq)sin2δ = Asin2δ.

13. The self and mutual inductances of a doubly excited magnetic system are Ls=0.6+0.20cos2θr H and Lr=0.75+0.30cos2θr H and Msr=0.8cosθr H. For a stationary rotor at an angular position of θr=60°,what is the magnitude of torque when the currents is=20A DC and ir=10A DC?
a) -233.88N-m
b) +233.88N-m
c) -467.76N-m
d) +467.76N-m

Explanation: For θr=60°; Ls, Lr, Msr and their derivatives with respect to θr have the following values:
Ls=0.50H, Lr=0.60H, Msr=0.40H, dLs/dθr=-0.3464, dLr/dθr=-0.52, dMsr/dθr=-0.693
Substituting the numerical values in Te = 1/2is2dLs/dθr+1/2ir2dLr/dθr+isrdMsr/dθr = -233.88N-m.

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