Electrical machines - transformers

In previous we gone through losses and efficiency.
Now,
2. Auto - Transformers

GATE-1. A 50 kVA, 33001230 V single-phase transformer is connected as an autotransformer shown in figure. The nominal rating of the autotransformer will be: [GATE-2004]
(a) 50.0 kVA.      (c) 717.4 kVA    
(b) 53.3 kVA.        (d) 767.4 kVA  

GATE-2. A single-phase 50 kVA, 250 V/500V two winding transformer has an efficiency of 95% at full load, unity power factor. If it is reconfigured as a 500V/750V autotransformer, its efficiency at its new rated load at unity power factor will be: [GATE-2007]
(a) 95.752%   (b) 97.851% 
(c) 98.276 %   (d) 99.241%

Statement for Linked Answer Questions Q 3 and Q 4 :
The figure above shows coils 1 and 2, with dot markings as shown, having 4000 and 6000 turns respectively. Both the coils have a rated current of 25 A. Coil 1 is excited with single phase, 400 V, 50 Hz supply.

GATE-3. The coils are to be connected to obtain a single-phase, 400, 1000V autotransformer to drive a load of 10 kVA.Which of the options given should be exercised to realize the required auto-transformer? [GATE-2009]
(a) Connect A and D; Common B  (b) Connect B and D; Common C
(c) Connect A and C; Common B 
(d) Connect A and C; Common D

GATE-4. In the autotransformer obtained in Question 3, the current in each coil is: [GATE-2009]
(a) Coil-1 is 25 A and Coil-2 is 10 A (b) Coil-1 is 10 A and Coil-2 is 25 A (c) Coil-1 is 10 A and Coil-2 is 15 A  (d) Coil-1 is 15 A and Coil-2 is 10 A.

IES-1. In case of auto-transformers, which of the following statements are correct? [IES-2001]
1. An auto-transformer requires less copper as compared to a conventional, 2-winding transformer of the same capacity. 2. An auto-transformer provides isolation between the primary and secondary windings
3. An auto-transformer has less leakage reactance as compared to the conventional, 2-winding transformer of the same capacity.

Select the correct answer using the codes given below:
(a) 1, 2 and 3.              (b) 1 and 2 (c) 1 and 3.                    (d) 2 and 3

IES-2. A two-winding transformer is used as an autotransformer. The kVA rating of the autotransformer compared to the two-winding transformer will be: [IES-2002]
(a) 3 times            (b) 2 times
(c) 1.5 times          (d) Same

IES-3. A two-winding transformer is converted into an auto-transformer. If we apply additive polarity and subtractive polarity for the connections, then the secondary voltage is 2640 V and 2160 V, respectively. What is the ratio of primary to secondary voltage of the original transformer? [IES-2006] (a) 66 : 54                   (b) 54 : 66
(c) 10 : 1                     (d) 1 : 10

IES-4. A single-phase, 10kVA,  2000/ 200V, 50Hz transformer is connected to form an auto transformer as shown in the figure given below. What are the values of V1 and I2, respectively?[ figure contains V2 is 2000V & I1 is 50A]
(a) 2200V, 55A         (b) 2200V, 45A  (c) 2000V, 45A         (d) 1800V, 45A

IES-5. If the wave form of the voltage impressed on the primary of a Y−Δ bank contains 5th harmonics, what are the wave forms of the resultant voltages of the primary and the secondary? [IES-2005]
  Primary                Secondary
(a) Peaked               Peaked
(b) Peaked               Flat-topped
(c) Flat-topped         Peaked
(d) Flat-topped        Flat-topped

IES-6. What is the efficiency of an auto-transformer in comparison to that of a two-winding transformer of the same rating? [IES-2006]
(a) Slightly less than that of a two-winding transformer
(b) Same as that of a two-winding transformer 
(c) More than that of a two-winding transformer
(d) As low as 1/5th of the efficiency of a two-winding transformer

IES-7.  What is the power transmitted inductively in an auto-transformer which supplies a load at 161 volts with an applied primary voltage of 230 volts? [IES-2009] 
(a) 35% of the input
(b) 70% of the input
(c) 15% of the input 
(d) 30% of the input

IES-8. What is the power transferred conductively from primary to secondary of an auto-transformer having transformation ratio of 0.8 supplying a load of 3 kW? [IES-2009]
(a) 0.6 kW                       (b) 2.4 kW (c) 1.5 kW                       (d) 0.27 kW

Extra Questions:

DIRECTION:
1.The following three items consist of two statements, one labelled as ‘Assertion A’ and the other labelled as ‘Reason R’. You are to examine these two statements carefully and decide if the Assertion A and the Reason R are individually true and if so, whether the Reason is a correct explanation of the Assertion. Select your answers to these items using the codes given below: Codes:
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false.
(d) A is false but R is true.

Assertion (A) : An auto-transformer is more efficient in transferring energy from primary to secondary circuit.
Reason (R) : Because it does both inductively and conductively.

Statement for Linked Answer Questions Q 2 and Q 3 :
The weight of transformer is W1 (copper weight).it is converted into auto-transdormer.
2. How much copper is going to save by conversion ?
a.K*W1               b. (1/K)*W1
c.(1-K)*W1          d. (1+K)*W1

3. How much copper is going to save by conversion ?
a.K*W1               b. (1/K)*W1
c.(1-K)*W1          d. (1+K)*W1

Statement for Linked Answer Questions Q 4and Q 5 :
An auto-transdormer suppiies a load of 3Kw at 115 volts at a unity power factor. If the applied primary voltage is 230 volts.
4. calculate the power transferred to the load inductively ?
a. 1.5Kw  b. 2Kw  c.1.8Kw  d.2.5Kw

5. calculate the power transferred to the load conductively ?
a. 1Kw  b. 1.5Kw  c.1.8Kw  d.2.5Kw

Statement for Linked Answer Questions Q6,Q7 and Q8 :
A 500kva, 50 Hz, single-phase, 6600/5000-V auto-transdormer, assuming following approximate values : e.m.f per turn 8V, maximum flux density 1.3 Wb/m^2

6. Determine the area of core ?
a. 255cm^2               b. 266cm^2
c. 277cm^2               d. 288cm^2

7. Number of turns on h.v side &
l.v side are :
a. 625 & 825              b. 825 & 625
c. 660 & 500              d. 500 & 600

8. The position of tapping point of transformer ?
a. 200 turns from low voltage end or 625 turns from common end.
b. 200 turns from high voltage end or 650 turns from common end.
c. Only  650 turns from common end
d. Only 200 turns from low/high voltage end

Answers :

GATE :
1.d 2.c 3.a  4.d

IES :
1.c  2.b  3.c  4.d  5.b  6.c  7.d  8.b

Extra Questions :
1.a  2.a  3.c  4.a 5.b  6.c  7.b 8.b

In this I have to attach some figures. I will complete it soon.....

Electrical machines-Transformers

Everytime I tried while googling of gate questions topic wise,never found useful data.I am trying blog about gate and IES previous questions (topic wise).I am starting with machines subject and in machines opening with transformers.

1. Transformer Losses and Efficiency

GATE-1. A single phase transformer has a maximum efficiency of 90% at 111 load and unity power factor. Efficiency at half load at the same power factor is: [GATE-2003]
(a) 86.7%      (c) 88.9%  
(b) 88.26%    (d) 87.8%

GATE-2. A 500 kVA, 3-phase transformer has iron losses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is:
[ GATE-2003]
(a) 50.0%      (b) 70.7% 
(c) 141.4%    (d) 200.0%

Data for Q.3 and Q.4 are given below. Solve the problems and choose the correct answers.

A 300 kVA transformer has 95% efficiency at full load 0.8 pf lagging and 96% efficiency at half load, unity pf.

GATE-3. The iron loss (Pi) and copper loss (Pc) in kW, under full load operation are: [GATE-2006]
(a) Pc= 4.12, Pi= 8.51    (b) Pc= 6.59, Pi = 9.21   (c) Pc= 8.51, Pi = 4.12    (d) Pc= 12.72, Pi = 3.07

GATE-4. What is the maximum efficiency (in %) at unity pf load? (a) 95.1   (b) 96.2  (c)96.4 (d)98.1
 

And now some IES based questions

IES-1. A single-phase transformer when supplied from 220V, 50Hz has eddy current loss of 50W. If the transformer is connected to a voltage of 330V, 50Hz, the eddy current loss will be: [IES-2001]
(a) 168.75W          (b) 112.5W
(c) 75W                  (d) 50W

IES-2.  If cP and scP represent core and full-load ohmic losses respectively, the maximum kVA delivered to load corresponding to maximum efficiency is equal to rated kVA multiplied by: [IES-2001]  (a) Pc /Psc 
(b) square root of Pc/Psc   
(c) Square of Pc/Psc    
(d) Square of Pc/Psc * Square of Psc/Pc

IES-3. The full-load copper-loss and iron-loss of a transformer are 6400W and 5000W respectively. The copper-loss and iron-loss at half load will be, respectively [IES-2002] 
(a) 3200 W and 2500 W  
(b) 3200 W and 5200 W  
(c) 1600 W and 1250 W  
(d) 1600 W and 5000 W 

DIRECTION:
The following three items consist of two statements, one labelled as ‘Assertion A’ and the other labelled as ‘Reason R’. You are to examine these two statements carefully and decide if the Assertion A and the Reason R are individually true and if so, whether the Reason is a correct explanation of the Assertion. Select your answers to these items using the codes given below: Codes: (a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

IES-4. Assertion (A): The distribution transformers are designed for minimum core losses. [IES-2002] 
Reason (R): Primary windings of distribution transformers are energized throughout the day. 

IES-5. If P1 and P2 be the iron and copper losses of a transformer at full load, and the maximum efficiency of the transformer is at 75% of the full load, then what is the ratio of P1 and P2 ? [IES-2006]  (a) 9/16  (b) 10/16 (c) 3/4 (d) 3/16 

IES-6. If the iron core of a transformer is replaced by an air core, then the hysteresis losses in the transformer will: [IES-2006] 
(a) Increase     (b) Decrease 
(c) Remain unchanged   
(d) Become zero 

IES-7. The equivalent circuit of a transformer has the leakage reactances X1, X2′ and the magnetising reactance Xm. What is the relationship between their magnitudes? [IES-2006]
(a) X1>>X′2>>Xm 
(b) X1<<X′2<< Xm 
(c) X1≈X′2>>Xm  
(d) X1≈X′2<< Xm

IES-8. If the voltage applied to a transformer primary is increased by keeping the V/f ratio fixed, then the magnetizing current and the core loss will, respectively, [IES-2006] 
(a) Decrease and remain the same  (b) Increase and decrease
(c) Remain the same and remain the same 
(d) Remain the same and increase 

IES-9. A 500 kVA transformer has constant losses of 500 Wand copper losses at full load are 2000 W. Then at what load, is the efficiency maximum? [IES-2007]
(a) 250 kVA        (b) 500 kVA
(c) 1000 kVA.     (d) 125 kVA

IES-10. On which of the following factors does hysteresis loss depend? [IES-2007]
1. Flux density   
2. Frequency  
3. Thickness of lamination 
4. Time 
Select the correct answer using the code given below:
(a) 2 and 3.           (b) 1 and 2
(c) 3 and 4              (d) 1 and 4 

IES-11. A single-phase transformer rated for 220/440 V, 50 Hz operates at no load at 220 V, 40 Hz. This frequency operation at rated voltage results in which one of the following? [IES-2008]
(a) Increase of both eddy-current and hysteresis losses 
(b) Reduction of both eddy-current and hysteresis losses 
(c) Reduction of hysteresis loss and increase in eddy-current loss 
(d) Increase of hysteresis loss and no change in the eddy-current loss 

IES-12. What is the load at which maximum efficiency occurs in case of a 100 kVA transformer with iron loss of 1kW and full-load copper loss of 2 kW? [IES-2008] 
(a) 100 kVA            (b) 70.7 kVA
(c) 50.5 kVA            (d) 25.2 kVA

IES-13. The full-load copper loss and iron loss of a transformer are 6400 Wand 5000 W, respectively. What are the above copper loss and iron loss, respectively at half-load? [IES-2008] 
(a) 3200 W, 2500 W   
(b) 3200 W, 5000 W 
(c) 1600 W, 1250 W   
(d) 1600 W, 5000 W
                                           
IES-14. When are eddy-current losses in a transformer reduced? [IES-2008]
(a) If laminations are thick
(b) If the number of turns in primary winding is reduced
(c) If the number of turns in secondary winding is reduced
(d) If laminations are thin

Some other questions

1. If cu loss of a transformer at 7/8 th full load is 4900 watts. then,its full-load cu loss would be
(a) 5600 (b) 6400 (c) 375 (d) 429

2. The iron loss of a transformer at 400 Hz is 10 watts.
Assuming the eddy current and hysteresis losses vary as the square of flux density,the iron loss of the transformer at rated voltage.but,at 50 Hz would be ........ Watts
(a) 80 (b) 640 (c) 1.25 (d) 100

3. A 200kva transformer has an iron loss of 1 KW and full-load CU loss of 2KW.its load kva corresponding to maximum efficiency is
(a) 100 (b) 141.4 (c) 50 (d) 200

4. The ordinary transformer has maximum efficiency when
(a) it runs at half-load
(b) it runs at full-load
(c) its cu-loss equal to iron-loss
(d) its runs slightly over load

5. Hysteresis loss depends on which factors ?
(a) flux density
(b) frequency
(c) quality of amount of iron in core
(d) All of the above

6. For distribution transformer, the increase in voltage effect the efficiency
(a) at any load increases [Fractional/Full-load/Over-load]
(b) at any load decreases
(c) at fractional load decreases & at full-load/over-load increases
(d) None of the above

7. For constant kva output is assumed,how will effect the cu-loss & regulation of a transformer by change in voltage
(a) varies as square of voltage.but, decreases with increase in voltage. (b) varies as voltage.but, decreases with increase in voltage.
(c) varies as square of voltage.but, increases with decrease in voltage. (d) varies as square of voltage.but, increases with decrease in voltage.

8. Iron loss of a transsformer changes with change in voltage as
(a) varies as square of voltage.
(b) varies as voltage.
(c) varies as 1/square of 'V'
(d) varies as 1/voltage

9. For constant kva output ,the increase in voltage will effect the heating of transformer as
(a) Iron temperature increases.
(b) copper temperature decreases.
(c) iron temperature increases & copper temperature decreases.
(d) iron temperature decreases & copper temperature increases.
(e) None of the above.

10. The increase in frequency of transformer will effect the iron losses
(a) Increases (b) decreases
(c) no change

11. The increase in frequency of transformer will effect the cu losses
(a) Increases (b) decreases
(c) no change

12. The decrease in frequency of transformer will effect the heating of transformer (temperature)
(a) Increases    (b) decreases
(c) no change    (d) independent

13. Efficiency of transformer at lower frequencies .............. compared with higher frequencies.
(a) Less (b) More (c) equal

14. On which of the following factors does eddy current loss depend?
1. Flux density   
2. Frequency  
3. Thickness of lamination 
4. Time 
Select the correct answer using the code given below:
(a) 2 and 3.           (b) 1,2 and 3
(c) 1 and 3            (d) 1 and 2

Answers for above questions:

GATE:
1. d  2. b  3. c  4. b

IES :
1.b  2.b  3.b  4.a  5.a  6.d  7.d  8.d 9.a  10.b   11.d.  12.b   13.d   14.d

Extra Questions :
1.b 2.b 3.b 4.c 5.c 6.c 7.a 8.a 9.c 10.b 11.a 12.a 13.a 14.b

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