Electrical Machine – I QB

QUESTION BANK

Department of Electrical & Electronics Engineering

Sub. Name with code: EE 2251 Electrical Machine – I   Class: II EEE

Problems

DC Generator

1.       A 4 pole dc generator running at 1 500 rpm has an armature with 90 slots and 6 conductors per slot.  The flux per pole is 10 mWb.  Determine the induced emf if the armature winding is (i) lap connected and (ii) wave connected.

2.       Determine the flux per pole for 6 pole dc machine having 240 wave connected conductors, which generates an open circuit voltage of 500 V while running at  1 000 rpm.

3.       A separately excited dc generator running at 1 000 rpm supplied 110 A at 220 V to a resistive load.  If the load resistance remains constant, what will be the load current if the speed is reduced at 800 rpm?  Armature resistance is 0.02 Ω.  Field current is unaltered.  Assume a voltage drop is 1 V per brush.  Ignore the effect of armature reaction.

4.       A 4 pole separately excited dc generator has a lap connected   armature with 480 conductors.  The armature resistance is 0.02 Ω.         With an output current of 400 A from the armature, the terminal              voltage is 230 V when the machine is driven at 900 rpm.           Determine the useful flux per pole.

5.       A 4 pole, lap wound, dc shunt generator has a useful flux per pole of 0.06 Wb. The armature winding consists of 220 turns each of 0.004 Ω resistance.  Calculate the terminal voltage and load current when it runs at 900 rpm, if the armature current is 50 A and field circuit resistance is 200 Ω.

6.       A dc shunt motor takes 110 A from 440 V supply.  The resistance of armature circuit is 0.2 Ω and that of field circuit is 220 Ω.  The machine has 6 poles and the armature is lap connected with 864 conductors.  The flux per pole is 0.06 Wb.  Calculate the speed.

7.       A 25 kW, 500 V dc series generator has armature and series field resistance of 0.05 Ω and 0.03 Ω respectively.  Calculate the generated emf and the armature current at full load.

8.       A 4 pole, 500 V dc series motor has 944 wave connected armature conductors.  The power input is 10 kW.  Flux per pole = 0.036 Wb; armature resistance = 0.5 Ω and series field resistance = 0.7 Ω. Determine the speed of operation.

9.       A short-shunt compound generator has armature, shunt field and series field resistance of 0.8 Ω, 50 Ω and 0.6 Ω respectively and supplies a load of 5 kW at 230 V. Calculate the emf generated in the armature.

10.    A long-shunt compound motor takes 100 A from 500 V supply.  Its armature, shunt field and series field resistance are 0.05 Ω, 250 Ω and 0.03 Ω respectively.  The brush drop is 1 V per brush arm.  Calculate the induced emf.

11.    An 8 pole dc shunt generator has 1 556 conductors, wave connected, in the armature and runs at 2 000 rpm.  The terminal voltage is 250 V and the load is 10 Ω.  The armature resistance is 0.5 Ω and the field resistance is 500 Ω.  Find the armature current and induced emf.

12.    A 250 V, 5 kW, 6 pole lap-wound shunt generator has shunt field and armature resistance of 250 Ω and 0.5 Ω respectively.  The generator supplies 100 lamps rated at 250 V, 40 W.  Allowing a brush drop of 1 V per brush, determine (i) the load current; (ii) the current in each parallel path of the armature and (iii) the emf generated in the armature.

13.    A 4 pole shut generator with lap wound armature supplied 2.4 kW at 120 V. The armature and field copper losses are 69 W and 200 W respectively.  Calculate the armature current and the generated emf.

14.    A 25 kW compound generator works on full load with a terminal voltage of 250 V.  The armature, series and shunt field resistance are 0.1 Ω, 0.05 Ω and 125 Ω respectively.  Calculate the generated emf when it is (i) long-shunt and (ii) short-shunt.

15.    A 4 pole, lap wound separately excited dc generator has an armature resistance of 0.4 Ω and is driven at 750 rom.  The armature has 720 conductors and the flux per pole is 0.03 Wb.  If the load resistance is 12 Ω, determine the terminal voltage of the machine.

16.     A separately excited dc generator, when driven at 1 500 rpm, supplies a load current of 200 A at 250 V to a circuit of constant resistance.  What will be the current and the voltage if the speed is reduced to 1 250 rpm keeping field current unaltered?  Armature resistance = 0.05 Ω; brush contact drop 2 V; neglect the effect of armature reaction.

17.    Estimate the percentage reduction in speed of a separately excited generator working with constant excitation on 400 V constant voltage bus-bars to decrease its load from 600 to 400 kW.  The machine resistance is 0.02 Ω.  Neglect armature reaction.

18.    A 4 pole lap connected dc shunt generator having field and armature resistance of 50 Ω and 0.15 Ω respectively supplies seventy five 200V, 60 W lamps.  Calculate the armature current, the current through the armature conductors and the induced emf.  Allow brush contact drop as 2 V.

19.    A 6 pole, wave wound, 500 rpm dc shunt generator has armature and field resistance of 0.5 Ω and 250 Ω respectively.  The armature has 250 conductors and the flux per pole is 40 mWb.  If the load resistance is 15 Ω, determine the terminal voltage and load current.

20.    A 4 pole dc shut generator has a wave connected armature.  The armature and shunt field resistance are 0.2 Ω and 50 Ω respectively.  If the generator supplies eighty, 200 V, 60 W lamps, find the generated emf, the total armature current and the current through each armature conductor.

DC Motor

1.       A 6 pole, 500 V dc motor has 720 wave connected conductors in its armature.  The full load armature current is 70 A and the flux per pole is 0.02 Wb.  The armature resistance is 0.2 Ω and the contact drop is 1 V per brush.  Calculate the full load speed.

2.       A 230 V dc shunt motor takes a total current of 25 A from the supply lines.  The resistance of the shunt field winding is 200 Ω and that of the armature is 0.3 Ω.  Find (i) the current in the armature and (ii) the back emf.

3.       A 110 kW, belt driven dc shunt generator driven at 375 rpm on 220 V bus-bars continues to run as a motor when he belt breaks, then taken a power of .5 kW.  Find its speed as a motor if the armature resistance is 0.025 Ω and the field resistance is 110 Ω.  Neglect armature reaction and take contact drop under each brush as 1 V.

1. (i) Derive an expression for the RMF value of EMF induced in a coil of N turns in the presence of time varying flux.
   (ii) Two coupled coils have self and mutual inductance of L₁₁ = 2 + 1 / (2x); L₂₂ = 1 + 1 / (2x); L₁₂ = L₂₁ = 1 / (2x).  Over a certain range of linear displacement x.  The first coil is excited by a constant current of 20 A and the second by a constant current of – 10 A.  Find (1) Mechanical work down if x changes from 0.5 to 1 m. (2) Energy supplied by each electrical source in part (1) and (3) Change in field energy in part (1)

                  

QUESTION BANK

Department of Electrical & Electronics Engineering

Sub. Name with code: EE 2251 Electrical Machine – I   Class: II EEE

UNIT – 1

PART – A

1.       What are the different parts of an electrical machine?

2. Give the principle of operation of a dc machine.
3. Give the classification of ac motors?
4. What is mmf?  Give its expression.
5. What is magnetic field strength?
6. Define reluctance.
7. What is leakage flux?
8.  Draw the magnetization curve of ferromagnetic material.
9. What is fringing effect?
10. Define stacking factor.
11. Compare electric and magnetic circuits.
12. What is electromagnetic induction?
13. Derive an equation for Lorentz force.
14. What is eddy current loss?
15. How to reduce hysteresis loss?
16. Define reluctance.
17. State Faraday’s first and second law.
18. Define permeance.
19. State Lenz’s law.

PART - B

1. (i) Define the terms self inductance and mutual inductance.   Derive the expression for the self and mutual inductance of two coils connected in series.[8]

(ii) When two coils are connected in series, their effective inductance is found to be 10 H.  When the connections of one coil are reversed, the effective inductance is 6 H.  If the coefficient of coupling is 0.6, calculate the self inductance of each coil and the mutual inductance. [8]

2. (i) Explain the two different types of magnetic circuits with neat diagram.[8]

3. (i) Write short notes on B-H loop.[8]

(ii) Explain in detail about A.C operation of magnetic circuits. [8]

4. (i) Explain the various types of core losses.[6]

(ii) Two mutually linked air-cored coils ‘a’ and ‘b’ have complete inductance la = 0.05 H and lb = 0.15 H.  Coil ‘a’ is excited and coil ‘b’ is left open.  It is found that when the current in coil a decreases at a uniform rate from 6 A to 1 A in 0.005 s a voltage of 60.6 V is induced in coil ‘b’.  Determine the mutual inductance and the coupling coefficient.[10]

5. (i) A steel ring has a mean diameter of 20 cm, a cross section of 25 cm² and a radial air gap of 0.8 mm cut across it.  When excited by a current of 1 A through a coil of 1 000 turns wound on the ring core, it produces an air gap flux of 1 mWb.  Neglecting leakage and fringing, calculate (a) relative permeability of steel and (b) total reluctance of the magnetic circuit.[8]

(ii) State and explain the two kinds of power losses that occur when a magnetic material under goes cyclic magnetization.[8]

6. (i) A straight conductors of 1.5 m length carries a current of 40 A.  It is lying at right angles to a uniform magnetic flux density of 0.8 T.  Find (a) the force developed on the conductor, (b) the power required to drive the conductor at a uniform speed of 25 m/s and (c) the emf induced in the conductor.[8]

(ii) Explain with the help of neat diagram about the nature of the magnetic field produced when a three phase supply is connected across a three phase winding.[8]

7. (i) Explain about the magnetization curve of ferro-magnetic material.[8]

(ii) Derive the relation between mutual inductance and self inductance of two magnetically coupled coils.[8]

8. (i) Explain in detail about hysteresis and eddy current losses.[6]

(ii) Two coupled coils have self and mutual inductance of L₁₁ = 3 + 1 / (3x); L₂₂ = 1 + 1 / (4x); L₁₂ = L₂₁ = 1 / (2x).  over a certain range of linear displacement x.  Find the expression for the time – average force of field origin at x = 0.6 m if: (1) both coils are connected in series across a voltage sources of 150 cos 314 t V. (2) both coils are connected in parallel across a voltage sources of 150 cos 314 t V.[10]

9. (i) The magnetic flux density on the surface of an iron face is 1.8 T which is a typical saturation level value for ferromagnetic material.  Find the force density on the iron face.[8]

(ii) T((ii) Two coupled coils have self and mutual inductance of L₁₁ = 3 + 1 / (3x); L₂₂ = 1 + 1 / (3x); L₁₂ = L₂₁ = 1 / (3x).  over a certain range of linear displacement x.  The first coil is excited by a constant current of 10 A and the second by a constant current of – 5 A.  Find the mechanical work down if x changes from 0.5 to 1 m and energy supplied by each electrical source for the above case[8]

10. (i) What do you mean by magnetic leakage and fringing?[8]

(ii) The field winding of a dc electromagnet is wound with 800 turns and has resistance of 40 Ω when exciting voltage is230 V. The magnetic flux around the coil is 0.004 Wb.  Calculate the self inductance of the coil and the energy stored in the magnetic field.[8]

UNIT – 2

PART- A

1.       What is a transformer?

2. Give few applications of transformers.
3. What is meant by step-up, step-down and one-to-one transformer?
4. Mention the different parts of a transformer.
5. Give the function of a conservator.
6. What material is used in the transformer core?
7. Differentiate between core-type and shell-type transformer.
8. Give the principle of operation of a transformer.
9. Compare iron-core and air-core transformer.
10. What is the purpose of drawing equivalent circuit?
11. Write the transformation ratio of the transformer.
12. List the various losses in the transformer.
13. What are the causes of stray loss?
14. What is the purpose of conducting open-circuit test?
15. Why transformer rating is in kVA?
16. What is all-day efficiency of a transformer?
17. Define regulation of a transformer.
18. What is an auto-transformer?
19. Mention the different types of 3 phase transformer connections.
20. Why is efficiency of transformers more than that of other rotating electrical machines?
21. A 1 000 kVA, 50 kV / 40 kV, single phase auto-transformer is fully loaded.  Find the current in the common section of the winding.

PART – B

1. (i) A 15 kVA, 2 000 / 200 V transformer has an iron loss of 250 W and full-load copper loss 350 W.  During the day it is loaded as follows:   

No. of Hours	Load	Power factor
9	¼  load	0.5
7	Full load	0.8
6	¾ load	1.0
2	No load	--

          

       

               

               Calculate the all-day efficiency.[8]

               (ii) Explain the working principle of auto transformer.[8]

2. (i) Explain in detail about the parallel operation of single phase transformers.[8]

(ii) Explain in detail about the phase conversion using transformers.[8]

3. (i) Derive the EMF equation of a transformer.[8]

(ii) A 5 kVA, 2 300 / 230 V, 50 Hz transformer was tested for the iron losses with normal excitation and copper losses at full load and these were found to be 40 W and 112 W respectively. Calculate the efficiencies of the transformer at 0.8 power factor for the following kVA outputs:  1.25, 2.5, 3.75, 5.0, 6.25 and 7.5.  Plot efficiency Vs kVA output curve.[8]

4. (i) Describe the procedure for conducting open-circuit and short-circuit tests on a single phase transformer.  How can the parameters be found from these tests?[8]

      (ii) Why are the tap-changing transformers required?  Explain the operation of no- load tap-changing transformer.[8]

5. (i) With neat sketch, explain the construction and principle of operation of single phase two winding transformers.[8]

(ii) The maximum efficiency of a 500 kVA, 3 300 V / 500 V, 50 Hz, single phase transformer is 97 % and it occurs at ¾ full load, unity power factor.  If the impedance is 10 %, calculate the regulation at full load, 0.8 power factor lagging.[8]

6. (i) Draw and explain the no-load phasor diagram of a single phase transformer.[8]

(ii) Derive expression for the current shared by two transformers operating in parallel, with unequal no-load voltages.[8]

7. (i) Obtain the equivalent circuit of a 200 / 400 V, 50 Hz, single phase transformer from the following test data:[8]

O.C. Test:              200V, 0.7 A, 70 W – on L.V. side

S.C. Test:                15 V, 10 A, 85 W – on H.V. side.

(ii) In a 25 kVA, 2 000 / 200 V, single phase transformer, the iron and full load copper losses are 350 W and 400 W respectively.  Calculate the efficiency at unity power factor on (a) full load and (b) half full load.[8]

8. (i) Explain the constructional details of core and shell type     transformers.[8]

(ii) Obtain the exact equivalent circuit of a single phase transformer.[8]

9. A 100 kVA, 1 000 / 10 kV, 50 Hz, single phase transformer has an iron loss of 1 100 W.  The copper loss with 5 A in the high voltage winding is 400 W.  Calculate the efficiency at (a) 25 % (b) 50 % and (c) 100 % of normal load for power factor of 1.0 and 0.8.  The output terminal voltage being maintained at 10 kV.  Find also the load for maximum efficiency at both power factors.[16]

10. (i) What is sumpner’s test? Draw the circuit diagram to conduct the test.[8]

            (ii)Explain Scott connection and explain in detail.[8]

UNIT – 3

PART - A

1. Write the expression of the energy absorbed by the magnetic system.
2. Give the expression for the energy density of the magnetic field.
3. What is the principle of energy conversion?
4. What is the purpose of single excited devices?
5. Give the function of electro-mechanical transducer.

6.       Draw the B-H curve of permanent magnet.

7. Give the expression for energy density in the electric field.
8. Draw a diagram of an abstracted electro-mechanical system.
9. What happens when an attracted armature relay is excited by an electric source?
10. Give the expression for mechanical power output of an electromechanical system.
                                             

PART – B

1. (i) Derive an expression for the magnetic torque developed in a doubly excited translation magnetic system.[8]

        (ii) The self and mutual inductances of the two exciting coils of multiply excited translatory system are: L₁₁ = L₂₂ = 3.6/(1 + 2x), L₁₂ = L₂₁ = 1.8 / (1 + 2x)  Calculate the time, average force and coil currents at x = 0.4 m when both the coils are connected in parallel across a voltage source of 100 cos 314 t.[8]

2. (i) Explain the concept of electromechanical energy conversion with neat diagram.[8]

(ii) Explain the concept of singly-excited machines and drive the expression for the electromagnetic torque.[8]

3. (i) Represent pictorially the flow of energy in electromechanical energy conversion devices for both generating and motoring action.[8]

(ii) Derive the expression for field energy, co-energy and the mechanical force in a single excited magnetic system.[8]

4. (i) Show that the torque developed in a double excited magnetic system is equal to the rate of increase of field energy with respect to displacement at constant currents.[8]

(ii) In a double excited rotary machine, the inductance coefficients are: L₁₁ = (1.1 + 0.4 cos 2θ); L₂₂ = (0.03 + 0.005 cos 2θ); L₁₂ = 0.2 cos θ.  The exciting currents are i₁ = 8 A, i₂ = 50 A.  Obtain the torque/angular displacement relation.[8]

5. (i) Show that the torque developed in doubly excited magnetic system is equal to the rate of increase of field energy with respect to displacement at constant current.[8]

(ii) The λ – I characteristics of single excited electromagnet is given by i = 121 λ²x² for 0 < i < 4 A and 0 < x < 10 cm.  If the air gap is 5 cm and a current of 3 A is flowing in the coil, calculate field energy, co-energy and mechanical force on the moving part.[8]

6. Explain in detail about energy in magnetic system.[16]

7. (i) With one example derive the co-energy of a multiply-excited magnetic field system.[8]

(ii) Two coupled coils have self and mutual inductance of  L₁₁ = 3 + 0.5x; L₂₂ = 2 + 0.5x; L₁₂ = L₂₁ = 0.3x  over a certain range of linear displacement x.  The first coil is excited by a constant current of 15 A and the second by a constant current of -8 A.  Find (1) Mechanical work down if x changes from 0.6 to 1 m.  (2) Energy supplied by each electrical source.[8]

8. Explain the i – λ characteristics if a magnetic system.  Also derive expression for co-energy density assumes the i – λ relationship of the magnetic circuit is linear.[16]

9. (i) Draw the diagram of a magnetic field system with two electrical excitations.[8]

(ii) Derive expression for mechanical force developed by magnetic field.[8]

10. (i) Derive an expression for co-energy density of an electromechanical energy conversion device.[8]

(ii) Consider at attracted armature relay is excited by an electric.  Explain about mechanical force developed and the mechanical energy output with necessary equations.  For linear and non linear cases.[8]

UNIT – 4

PART - A

1. What is armature winding?
2. What is full-pitched?
3. Derive an equation for flux linking the coil of synchronous machine.
4. Give the expression of the emf induced in the coil of a synchronous machine.
5. How is the number of slots per pole per phase of a synchronous machine calculated?
6. What is a two-layer winding?
7. How is the mmf change art a slot expressed?
8. Write the expression to calculate the speed of a rotating mmf.
9. How is mmf across air-gap expressed?
10. Write the expression for torque developed in a synchronous motor.
11. Show how the two coils of 4 pole generator are connected in series and parallel connection.
12. Give the expression for torque developed in round rotor machine.
13. Distinguish between electrical angle and mechanical angle in an electrical machine.
14. Define phase spread and distribution factor.

PART – B

1. (i)Explain the various concepts of magnetic fields in rotating machines.[8]

(ii) Explain about mmf space wave of one phase of a distributed winding[8].

2. (i) Explain with neat diagram the concept of MMF space wave of a single coil.[8]

(ii) Explain the production of torque in synchronous machines (motoring).[8]

3. (i) Explain the concept of rotating magnetic fields in AC machines.[8]

(ii) A 3 phase, 50 Hz star connected alternator with 2 layer winding is running at 600 rpm. It has 12 T/coil, 4 slots / pole / phase and a coil-pitch of 10 slots.  If the flux per pole is 0.035 Wb sinusoidal distributed, find the phase and line emf induced. Assume that the total T/P are series connected.[8]

4. (i) Show that the net electromagnetic torque developed is zero if the rotating electrical machine has different number of poles on its stator and rotor.[8]

(ii) Derive an expression for torque developed in a 2-pole round rotor machine and state the assumptions made.[8]

5. (i) Derive an expression for the generated emf in synchronous machine.[8]

(ii) Determine the breadth and pitch factors for a 4 pole, 3 phase winding with 2 slots / pole / phase coil span in 5 slot pitches.[8]

6. (i) Derive an expression for induced emf in a synchronous machine.[8]

(ii) Explain the constructional features of elementary synchronous machines.[8]

7. Write in detail about the mmf space wave of three phase distributed winding.[16]

8. Explain mmf of distributed ac windings.[16]

9. Derive an expression for torque developed in round rotor machine in terms of the resultant flux / pole due to super imposition of the stator and rotor mmf.  Also state if any assumption is made.[16]

UNIT – 5

PART - A

1. Define pole pitch.
2. What is back pitch and front pitch?
3. Write the emf equation of dc generator explaining all terms.
4. State the principle of operation of dc motor.
5. What is rotating torque?
6. Obtain an expression for armature torque.
7. What is armature reaction?  What are its effects?
8. Mention the different types of dc generators.
9. Give the types of compound generators.
10. What are the characteristics of dc generators?
11. Draw the external characteristics of a shunt generator.
12. Mention the uses of dc generators.
13. Mention the application of various dc motor.
14. List out the factors that control the speed of a dc motor.
15. Give few applications of Ward-Leonard systems.
16. Why is starter needed to start the dc motor?

PART – B

1. (i) What is meant by circuit model of dc machine?  Explain them in detail. [8]

(ii) Explain the various methods of excitation of dc machines.[8]

2. (i) Explain the method of speed control of dc motors with field control.[8]

        (ii)With neat circuit diagram explain the conduction of Swinburne’s test and also explain the efficiency calculation as generator.[8]

3. Explain the construction of dc machine with neat diagram.[16]

4. (i) Draw the diagram of 3 point starter and explain its working.[8]

        (ii) A 440 V dc shunt motor takes 4 A at no load.  Its armature and field resistance are 0.4 Ω and 2 220 Ω respectively.  Estimate the kW output and efficiency when the motor takes 60 A on full load.[8]

5. (i) Derive the expression for the torque developed in the armature of a dc motor.[8]

(ii) Draw and explain the different characteristics of a dc shunt motor.[8]

6. (i)Describe the effects of armature reaction on the operation of dc machines. Describe also the remedies employed for decreasing the effects of armature reaction.[8]

(ii) A 500 V, dc shunt motor takes a total current of 5 A when running unloaded.  The resistance of armature circuit is 0.25 Ω and the field resistance is 125 Ω.  Calculate the efficiency and output when the motor is loaded and draws a current of 100 A.[8]

7. (i) Explain the speed-torque characteristics of dc shunt and dc series motors.[6]

        (ii) A 230 V, dc shunt motor, takes an armature current at 3.33 A at rated voltage and at a no-load speed of 1 000 rpm.  The resistances of the armature circuit and field circuit are 0.3 Ω and 160 Ω respectively. The line current at full load and rated voltages is 40 A.  Calculate, at full load, the speed and the developed torque in case the armature reaction weakens the no-load flux by 4 %.[10]

8. (ii) Explain the various losses which take place in a dc machine.[8]

(ii) Two separately-excited dc generators are connected in parallel and supply a load of 200 A.  The machines have armature circuit resistance of 0.05 Ω and 0.1 Ω and induced emf of 425 V and 440 V respectively.  Determine the terminal voltages, current and power output of each machine.  The effect of armature reaction is to be neglected.[8]

9. (i) Derive an expression for the emf generated in the armature winding of a dc machine.[8]

        (ii) A long-shunt compound generator delivers a load current of 50 A at 500 V and has armature, series field and shunt field resistances of 0.05 Ω, 0.03 Ω and 250 Ω respectively.  Calculate the generated voltage and the armature current.  Allow IV per brush for contact drop.[8]

10.    Two dc generators are connected in parallel to supply a load of 1 500 A.  One generator has an armature resistance of 0.5 Ω and an emf of 400 V while the other has an armature resistance of 0.04 Ω and an emf of 440 V.  The resistances of shunt fields are 100 Ω and 80 Ω respectively.  Calculate the current supplied by the individual generators and the terminal voltage.[16]

11.    (i) Derive the condition to obtain maximum efficiency of dc machines[8].

(ii) A 60 kW, 400 V, dc shunt motor has 4 poles and a wave connected armature of 150 conductors.  The flux per pole is 45 mWb. R_a = 0.1 Ω and R_sh = 200 Ω.  If the full load efficiency is 90.5 %, find the speed, armature torque and useful torque.[8]