DC and AC Machines

What to remember

• A generator changes mechanical energy to electrical energy; a motor does the opposite. Both work on electromagnetic induction (Faraday) and the force on a current-carrying conductor.
• DC machines use a commutator; AC machines use slip rings or none. Induction motors are the most used motors in industry and farms.
• Transformers change voltage level at the same frequency. Turns ratio decides the output voltage.

Basic laws

• Faraday's law: an emf is induced in a coil when the magnetic flux linked with it changes. e = −N dΦ/dt.
• Lenz's law: the induced current opposes the change that causes it.
• Fleming's right-hand rule: gives direction of induced emf (generator). Thumb is motion, forefinger is field, middle finger is current.
• Fleming's left-hand rule: gives direction of force on a conductor (motor).
• Force on a conductor in a field: F = B I L (when the conductor is at right angles to the field).
• Units: flux in weber (Wb), flux density in tesla (T).

DC generators

Main parts: yoke (frame), field poles with field winding, armature core with armature winding, commutator (converts the alternating emf in the armature to a unidirectional output), and brushes (carbon, collect current).

Emf equation: E = (P Φ Z N)/(60 A), where P is number of poles, Φ is flux per pole, Z is total armature conductors, N is speed in rpm, and A is number of parallel paths. For a lap winding A = P; for a wave winding A = 2.

Worked example: P = 4, Φ = 0.02 Wb, Z = 400, N = 1200 rpm, lap winding (A = 4): E = (4 × 0.02 × 400 × 1200)/(60 × 4) = 38400/240 = 160 V.

Self-excited generators need residual magnetism to build up voltage. Armature reaction is the effect of the armature field on the main field. Interpoles reduce sparking at the brushes.

DC motors

When a current-carrying armature is in a magnetic field, a torque is produced. As the armature turns, it cuts flux and induces a back emf Eb that opposes the supply. Voltage equation: V = Eb + Ia Ra. Armature current Ia = (V − Eb)/Ra. Torque T ∝ Φ Ia. Speed N ∝ Eb/Φ.

Worked example: V = 220 V, Ra = 0.5 Ω, Ia = 20 A. Eb = 220 − 20 × 0.5 = 210 V.

At starting, the speed is zero, so Eb is zero and the current would be V/Ra, very large. Therefore a starter (a series resistance, such as a three-point starter) is used to limit starting current.

Speed control: field (flux) control for speeds above normal, armature (resistance or voltage) control for speeds below normal. Reversing direction needs reversal of either the armature or field current, not both. Efficiency = output/input × 100. Losses: copper loss, iron loss (hysteresis and eddy current), mechanical loss.

Transformers

A transformer is a static device that transfers AC power between two circuits by mutual induction, with no change of frequency. It has a laminated core (silicon steel, to cut eddy current loss) and two windings: primary and secondary.

Turns ratio: V1/V2 = N1/N2 = I2/I1 (ideal). Example: a 2000-turn primary on 220 V and a 100-turn secondary give 220 × 100/2000 = 11 V (step-down). EMF equation: E = 4.44 f N Φm. A step-up transformer has more secondary turns; a step-down has fewer. A transformer does not work on DC. Kinds: power transformer, distribution transformer, instrument transformers (CT and PT), autotransformer (single winding). Losses: iron loss (fixed, from the core) and copper loss (varies with load). Efficiency is highest when iron loss equals copper loss. Rating is given in kVA, not kW, because the load power factor is not known. Cooling is by oil or air. Regulation = (no-load voltage − full-load voltage)/no-load voltage.

Three-phase induction motors

A three-phase supply in the stator winding creates a rotating magnetic field. Synchronous speed Ns = 120 f / P rpm. Example: 50 Hz, 4 poles give Ns = 120 × 50/4 = 1500 rpm. The rotor can never reach Ns; the difference is the slip. Slip s = (Ns − N)/Ns. If N = 1440 rpm, slip = 60/1500 = 0.04 or 4%.

Two types of rotor: squirrel cage (simple, rugged, cheap, most common) and slip ring or wound rotor (external resistance can be added for high starting torque and speed control). Starting methods for squirrel cage motors: direct on line (small motors), star-delta starter, autotransformer starter. In star-delta starting, the motor starts in star and runs in delta; this cuts the starting current to one-third of the direct-on-line value. Reversing direction needs the swap of any two supply lines. Applications: pumps, mills, lifts, and agricultural pumpsets.

Single-phase motors and special machines

A single-phase induction motor has no self-starting torque, so it needs an extra mechanism:

• Split-phase motor: start winding with a centrifugal switch (fans, washing machines).
• Capacitor-start motor: high starting torque (compressors, pumps).
• Capacitor-start capacitor-run / permanent split capacitor: ceiling fans.
• Shaded-pole motor: low cost, very small torque (small fans, record players).
• Universal motor: a series motor that runs on AC or DC at high speed (mixers, drills, vacuum cleaners).

Other machines: stepper motors move in fixed steps (printers, robots) and BLDC motors have no brushes (modern fans, drones).

Alternators and synchronous machines

An alternator (synchronous generator) makes AC. Frequency f = P N/120, with N as speed in rpm. A 4-pole alternator at 1500 rpm gives 50 Hz. The rotor carries the DC field and the stator carries the armature winding; keeping the high-voltage winding on the fixed stator makes it easy to insulate and to take out large currents. Large power stations use turbo-alternators (cylindrical rotor, high speed) in steam plants and salient pole alternators (low speed) in hydro plants. A synchronous motor runs at exact synchronous speed, is not self-starting, and can improve power factor when over-excited (used as a synchronous condenser).

Quick comparison of machine types

Power flow and efficiency: for a motor, input power = V × I, and output power = input minus losses. For a transformer, an ideal unit has input VA equal to output VA. Worked example: a 5 kVA transformer at 230 V can give a full-load current of 5000/230, about 21.7 A. Worked example: a motor takes 1000 W and gives 800 W, so efficiency is 800/1000 × 100 = 80%. Torque and power are related by P = 2π N T / 60 (N in rpm, T in newton-metres). Direct on line starting suits only small motors, because the starting current of an induction motor may be five to seven times the full-load current. Maintenance basics: keep brushes and commutators clean, check bearing lubrication, check insulation resistance with a megger, and keep transformer oil clean and dry.

Exam traps

• Generator and motor rules: right-hand rule for generators; left-hand rule for motors.
• Commutator and slip rings: a commutator gives DC; slip rings give AC output.
• Lap and wave: lap has A = P; wave has A = 2.
• Back emf and supply voltage: back emf is always less than the supply in a motor.
• Series motor at no load: it can run dangerously fast.
• Transformer on DC: it does not work, as no changing flux is produced.
• kVA and kW: transformer rating is in kVA.
• Synchronous speed and rotor speed: an induction motor runs below synchronous speed.
• Squirrel cage and slip ring: the slip ring type allows external resistance.
• Alternator frequency and motor slip: the alternator frequency depends on speed and poles; slip belongs to induction motors.

One-liners

• 1. A commutator makes the DC generator output unidirectional.
• 2. Back emf limits armature current in a DC motor.
• 3. A starter is needed because starting current is high.
• 4. The DC series motor has the highest starting torque.
• 5. A transformer works on mutual induction.
• 6. Transformer core is laminated to cut eddy current loss.
• 7. Ns = 120 f / P.
• 8. Slip = (Ns − N)/Ns.
• 9. The squirrel cage rotor is the most used type.
• 10. Swapping two lines reverses a three-phase motor.
• 11. A synchronous motor is not self-starting.
• 12. Alternator frequency f = P N / 120.

Practice questions

1. A 4-pole lap-wound DC generator has flux 0.02 Wb per pole, 400 conductors and runs at 1200 rpm. The generated emf is

   1. 640 V
   2. 160 V
   3. 80 V
   4. 320 V
   Answer

   B. 160 V

   E = P x flux x Z x N/(60 A) = 4 x 0.02 x 400 x 1200/(60 x 4) = 160 V.

2. A DC motor on 220 V has armature resistance 0.5 ohm and armature current 20 A. The back emf is

   1. 230 V
   2. 210 V
   3. 220 V
   4. 10 V
   Answer

   B. 210 V

   Eb = V - Ia Ra = 220 - 10 = 210 V.

3. A DC motor has armature resistance 0.5 ohm and is switched on to 220 V at standstill without a starter. The starting current is

   1. 220 A
   2. 44 A
   3. 110 A
   4. 440 A
   Answer

   D. 440 A

   At standstill Eb = 0, so I = 220/0.5 = 440 A.

4. A 230 V DC motor with Ra = 0.5 ohm has back emf 220 V. The armature current is

   1. 460 A
   2. 20 A
   3. 10 A
   4. 5 A
   Answer

   B. 20 A

   Ia = (230 - 220)/0.5 = 20 A.

5. A transformer has 2000 primary turns, 100 secondary turns and a 220 V primary supply. The secondary voltage is

   1. 22 V
   2. 110 V
   3. 440 V
   4. 11 V
   Answer

   D. 11 V

   V2 = 220 x 100/2000 = 11 V.

6. A transformer has 500 primary turns and 50 secondary turns on a 400 V supply. The secondary voltage is

   1. 40 V
   2. 200 V
   3. 4000 V
   4. 80 V
   Answer

   A. 40 V

   V2 = 400 x 50/500 = 40 V.

7. An ideal 1:10 step-up transformer has 2 A in the primary. The secondary current is

   1. 20 A
   2. 0.2 A
   3. 2 A
   4. 10 A
   Answer

   B. 0.2 A

   Currents are in inverse ratio to turns: 2/10 = 0.2 A.

8. A 5 kVA, 230 V single-phase transformer has a full-load current of about

   1. 1150 A
   2. 2.17 A
   3. 46 A
   4. 21.7 A
   Answer

   D. 21.7 A

   I = 5000/230 = 21.7 A.

9. A transformer has 100 turns on the primary, peak flux 0.01 Wb and frequency 50 Hz. The primary emf is (use 4.44)

   1. 222 V
   2. 111 V
   3. 22.2 V
   4. 444 V
   Answer

   A. 222 V

   E = 4.44 x f x N x flux = 4.44 x 50 x 100 x 0.01 = 222 V.

10. The synchronous speed of a 4-pole motor on a 50 Hz supply is

    1. 1000 rpm
    2. 1500 rpm
    3. 3000 rpm
    4. 750 rpm
    Answer

    B. 1500 rpm

    Ns = 120 x 50/4 = 1500 rpm.

11. The synchronous speed of a 6-pole motor on a 50 Hz supply is

    1. 1500 rpm
    2. 500 rpm
    3. 1000 rpm
    4. 750 rpm
    Answer

    C. 1000 rpm

    Ns = 120 x 50/6 = 1000 rpm.

12. A 4-pole induction motor on 50 Hz runs at 1440 rpm. The slip is

    1. 1.44%
    2. 6%
    3. 2%
    4. 4%
    Answer

    D. 4%

    Slip = (1500 - 1440)/1500 = 0.04.

13. A 6-pole induction motor on 50 Hz runs at 960 rpm. The percentage slip is

    1. 6%
    2. 4%
    3. 2%
    4. 0.4%
    Answer

    B. 4%

    Ns = 1000; slip = 40/1000 = 4%.

14. The frequency of a 4-pole alternator running at 1500 rpm is

    1. 50 Hz
    2. 60 Hz
    3. 100 Hz
    4. 25 Hz
    Answer

    A. 50 Hz

    f = P N/120 = 4 x 1500/120 = 50 Hz.

15. The speed needed by an 8-pole alternator to give 50 Hz is

    1. 1500 rpm
    2. 3000 rpm
    3. 750 rpm
    4. 375 rpm
    Answer

    C. 750 rpm

    N = 120 f/P = 120 x 50/8 = 750 rpm.

16. A motor takes 1000 W and delivers 800 W. Its efficiency is

    1. 20%
    2. 125%
    3. 8%
    4. 80%
    Answer

    D. 80%

    Efficiency = 800/1000 x 100 = 80%.

17. A conductor of length 0.2 m carries 10 A at right angles to a 0.5 T field. The force on it is

    1. 10 N
    2. 1 N
    3. 0.1 N
    4. 2 N
    Answer

    B. 1 N

    F = B I L = 0.5 x 10 x 0.2 = 1 N.

18. Star-delta starting reduces the line current at starting to what fraction of direct-on-line starting?

    1. One-half
    2. Two-thirds
    3. One-fourth
    4. One-third
    Answer

    D. One-third

    Star connection reduces the starting current to one-third.

19. Which rule gives the direction of induced emf in a generator?

    1. Fleming's left-hand rule
    2. Ohm's rule
    3. Fleming's right-hand rule
    4. Right-hand screw rule only
    Answer

    C. Fleming's right-hand rule

    Right hand is for generators; left hand is for motors.

20. Which rule gives the direction of force on a conductor in a motor?

    1. Fleming's left-hand rule
    2. Kirchhoff's rule
    3. Fleming's right-hand rule
    4. Lenz's rule
    Answer

    A. Fleming's left-hand rule

    The left-hand rule applies to motors.

21. Lenz's law states that the induced current

    1. aids the change that produces it
    2. opposes the change that produces it
    3. is always zero
    4. flows only in a straight wire
    Answer

    B. opposes the change that produces it

    This follows from conservation of energy.

22. The part of a DC machine that converts the alternating armature emf to unidirectional output is the

    1. interpole winding
    2. yoke
    3. slip ring
    4. commutator
    Answer

    D. commutator

    The commutator acts as a mechanical rectifier.

23. Carbon brushes in a DC machine are used to

    1. collect current from the commutator
    2. insulate the shaft
    3. cool the yoke
    4. produce the flux
    Answer

    A. collect current from the commutator

    Brushes carry current between the commutator and the external circuit.

24. Sparking at brushes in a DC machine is reduced by

    1. a larger air gap in the shaft
    2. a thinner shaft
    3. interpoles
    4. removing the field
    Answer

    C. interpoles

    Interpoles help commutation.

25. A starter is used with a DC motor because

    1. the speed is too low
    2. the motor has no field
    3. starting current would be very high with zero back emf
    4. the supply is AC
    Answer

    C. starting current would be very high with zero back emf

    At standstill Eb = 0.

26. Which DC motor has the highest starting torque and is used in traction?

    1. Synchronous motor
    2. Shunt motor
    3. Induction motor
    4. Series motor
    Answer

    D. Series motor

    Torque is proportional to the square of current in a series motor.

27. Which DC motor runs at nearly constant speed?

    1. Shunt motor
    2. Stepper motor
    3. Series motor
    4. Universal motor
    Answer

    A. Shunt motor

    The shunt motor has nearly constant speed from no load to full load.

28. Why should a DC series motor never be started without load?

    1. It will not turn
    2. It can reach a dangerously high speed
    3. It will draw no current
    4. Its field will reverse
    Answer

    B. It can reach a dangerously high speed

    With little load, flux is low and speed rises sharply.

29. A transformer does not work on DC because

    1. the voltage is too low
    2. the core is laminated
    3. the windings are copper
    4. there is no changing flux
    Answer

    D. there is no changing flux

    An emf is induced only by changing flux.

30. The core of a transformer is laminated to reduce

    1. friction loss
    2. windage loss
    3. eddy current loss
    4. copper loss
    Answer

    C. eddy current loss

    Thin insulated sheets cut eddy currents.

31. Transformer rating is given in kVA because

    1. copper loss is zero
    2. the load power factor is not known
    3. it is a DC machine
    4. iron loss is zero
    Answer

    B. the load power factor is not known

    Heating depends on voltage and current, not on the power factor.

32. The rotor type most widely used in three-phase induction motors is

    1. squirrel cage
    2. salient pole
    3. slip ring
    4. wound field
    Answer

    A. squirrel cage

    It is simple, rugged and cheap.

33. How can the direction of rotation of a three-phase induction motor be reversed?

    1. Increase the frequency
    2. Interchange any two supply lines
    3. Reduce the voltage
    4. Interchange all three lines
    Answer

    B. Interchange any two supply lines

    This reverses the rotating field.

34. Which single-phase motor has high starting torque and is used for compressors?

    1. Universal motor
    2. Reluctance generator
    3. Capacitor-start motor
    4. Shaded-pole motor
    Answer

    C. Capacitor-start motor

    A capacitor-start motor gives good starting torque.

35. Which motor can run on both AC and DC supply?

    1. Universal motor
    2. Squirrel cage motor
    3. Synchronous motor
    4. Capacitor-start motor
    Answer

    A. Universal motor

    A universal motor is a series-wound motor used in mixers and drills.

36. Statement 1: A DC generator uses a commutator. Statement 2: An alternator gives AC output. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

37. Statement 1: In a lap winding the number of parallel paths equals the number of poles. Statement 2: In a wave winding the number of parallel paths is 2. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

38. Statement 1: Back emf in a DC motor opposes the supply voltage. Statement 2: Back emf is greater than the supply voltage in normal running. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Back emf is less than the supply; the difference drives the armature current.

39. Statement 1: An induction motor runs at exactly synchronous speed. Statement 2: A synchronous motor runs at synchronous speed. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    An induction rotor always runs a little below synchronous speed.

40. Statement 1: A synchronous motor is self-starting. Statement 2: A single-phase induction motor needs a special starting arrangement. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    A synchronous motor is not self-starting.

41. Statement 1: Iron loss in a transformer is nearly constant. Statement 2: Copper loss varies with the load current. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are correct.

42. Statement 1: Maximum efficiency of a transformer occurs when iron loss equals copper loss. Statement 2: A transformer changes the frequency of the supply. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Frequency remains the same.

43. A 4-pole induction motor on a 50 Hz supply has a slip of 5%. Its speed is

    1. 1500 rpm
    2. 1475 rpm
    3. 1575 rpm
    4. 1425 rpm
    Answer

    D. 1425 rpm

    N = Ns(1 - s) = 1500 x 0.95 = 1425 rpm.

44. Which part of a power transformer carries the changing flux between the two windings?

    1. Bushing
    2. Breather
    3. Conservator tank
    4. Laminated core
    Answer

    D. Laminated core

    The core links the primary and secondary flux.

45. Statement 1: A step-up transformer has more turns on the secondary than on the primary. Statement 2: A step-up transformer increases the current as well as the voltage. Which of the statements is/are correct?

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    Voltage rises and current falls in a step-up transformer.