# Electrical Machines Questions and Answers – EMF Polygon – 2

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This set of Electrical Machines Multiple Choice Questions & Answers (MCQs) focuses on “EMF Polygon – 2”.

1. The winding’s for a 3-phase alternator are:

```(i) 36 slots, 4 poles, span 1 to 8
(ii) 72 slots, 6 poles, span 1 to 10
(iii) 96 slots, 4 poles, span 1 to 21
```

The winding’s having pitch factor of more than 0.97 are __________
a) (i) and (ii) only
b) (ii) and (iii) only
c) (i) and (iii) only
d) (i),(ii) and (iii)

Explanation: Kp=cosε/2
(i) Slots per pole = 36/4=9, for a coil span of 8 slots, the coil is short pitched by 1 slot and the chording angle is ε=γ = 20° ⇒ Kp=cos10°=0.985
(ii) Slots per pole = 72/6=12, for a coil span of 10 slots, the coil is short pitched by 2 slots and the chording angle is ε=2γ and γ=180/12 ⇒ ε = 30° ⇒ Kp=cos15°=0.9659
(iii) Slots per pole = 96/4=24, for a coil span of 21 slots, the coil is short pitched by 3 slots and the chording angle is ε=3γ and γ=180/24 ⇒ ε = 24.5° ⇒ Kp=cos12.25°=0.97723.

2. In 48 slot, 4-pole,3 phase alternator, the coil-span is 10. Its distribution and pitch factors are respectively ____________
a) 0.9717,0.966
b) 0.9822, 0.9814
c) 0.9577, 0.9814
d) 0.9577, 0.966

Explanation: Slots per pole = 48/4=12, for a coil span of 10 slots, the coil is short pitched by 2 slots and the chording angle is ε=2γ and γ=180/12 ⇒ ε = 30° ⇒ Kp=cosε/2=0.9659.
We know, Kd=(sin(qγ/2))/qsin(γ/2), here q=48/4∗3 = 4 ⇒ Kd=0.957662.
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3. A 3-phase, 4-pole alternator has 48 stator slots carrying a 3-phase distributed winding. Each coil of the winding is short chorded by one slot pitch. The winding factor is given by ______________
a) (cos7.5)/16
b) (cot7.5)/8
c) 1/(8sin7.5)
d) (cot7.5)/16

Explanation: Slots per pole = 48/4 = 12 ⇒ γ=180/12=15° and q=48/4∗3=4
coil of the winding is short chorded by one slot pitch ⇒ ε=γ=15°, Kw=Kp∗Kd = cos7.5(sin(4∗15/2))/(4∗sin(15/2)) = (cot7.5)/8.

4. The chording angle for eliminating 5th harmonic should be ____________
a) 30°
b) 34°
c) 36°
d) 35°

Explanation: To eliminate 5th harmonic kp5 must be zero, kpn = cosnε/2 ⇒ kp5 = cos5ε/2=0=cos90° ⇒ 5ε/2=90° ⇒ ε = 36°.
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5. Which of the following statements are true?

```(i) breadth factor for third harmonic kd3 is more than that for fundamental kd1
(ii) kd3 < kd1
(iii) kd3 may be less or more than kd1 depending upon the number of slots and poles
(iv) coil-span factor for third harmonic kp3>kp1 (coil span factor for fundamental)
(v) kp3 < kp1
(vi) kp3 may be less or more than kp1 depending upon the number of slots and poles
```

a) (ii), (v)
b) (i), (iv)
c) (iii), (vi)
d) (i), (iii), (iv), (vi)

Explanation: Examples will show that kdn < kd1 and has the effect of reducing the nth harmonic EMF in comparison with the fundamental EMF, similarly kpn < kp1.

6. A 6-pole alternator with 36 slots carries a 2-phase distributed winding. Each coil is short pitched by one slot. The winding factor is given by _____________
a) cot15°/3√2
b) cot15°/4
c) cot15°/2√2
d) cot15°/4

Explanation: Slots per pole = 36/6=6, q=6/2=3 ⇒ γ=180°/6=30°, coil is short pitched by one slot ⇒ ε=γ=30° and Kp=cosε/2=cos15° and Kd=sin(γq/2)/q(sinγ/2)=sin45/(3sin15)
Kw=Kp∗Kd=cot15°/3√2.

7. For eliminating nth harmonic from the EMF generated in the phase of a 3-phase alternator, the chording angle should be ______________
a) n∗full pitch
b) (1/n)∗full pitch
c) (2/n)∗full pitch
d) (3/n)∗full pitch

Explanation: kpn=cosnε/2=0 ⇒ nε/2=90° ⇒ ε=180°/n=full pitch/n.

8. Which among the given harmonics are called belt harmonics?
a) 5, 7, 11, 13
b) 3, 6, 9, 12
c) 5, 6, 11, 12
d) 7, 11, 13, 15

Explanation: The odd harmonics of the order 5, 7, 11, 13 etc are called belt harmonics.

9. Machine A has 60° phase spread and machine B has 120° phase spread. Both the machines have uniformly distributed winding. The ratio of distribution factors of machine A to machine B is ____________
a) 0.866
b) 1.1
c) 1.55
d) 1.155

Explanation: kdA=(sinσ/2)/σ/2, σ=60° ⇒ kdA=0.9556
kdB=(sinσ/2)/σ/2, σ=120° ⇒ kdB=0.827
thus, kdA/kdB=1.155.

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