DC Machines: DC Generator & DC Motor – Construction, EMF Equation, Back EMF, Types & Speed Control (with MCQs)

DC machines may look old-fashioned beside inverters and induction motors, but they are still a core topic in every electrical machines paper — and a goldmine of exam questions in PGCB, BPDB, BREB/PBS, DPDC, Bangladesh Railway, BCS (EEE) and viva boards: EMF equation, back EMF, why a series motor must never run without load, why a starter is needed, and how to control speed. This post explains them with a commutator animation, solved problems and MCQs.

⚡ Key takeaways

• The same machine can work as a generator (mechanical → electrical, Fleming’s right-hand rule) or a motor (electrical → mechanical, Fleming’s left-hand rule).
• The EMF induced in the armature coil is AC; the commutator converts it to DC at the brushes.
• EMF equation: E = PΦZN / 60A (A = P for lap, A = 2 for wave winding).
• Motor: back EMF E_b = V − I_aR_a; speed N ∝ E_b/Φ; torque T ∝ ΦI_a.
• Types: separately excited, shunt, series, compound. Series motor: very high starting torque but never start without load.

📑 Contents

1. Construction
2. DC generator: working and commutation (animation)
3. EMF equation
4. DC motor: working, back EMF and torque
5. Types of DC machines
6. Motor characteristics and applications
7. Why a starter is needed
8. Speed control
9. Losses and efficiency
10. Solved problems
11. Practice MCQs
12. বাংলায় দ্রুত রিভিশন

1. Construction

Part	Material	Function
Yoke (frame)	Cast iron / rolled steel	Mechanical support; carries magnetic flux between poles
Poles & pole shoes	Laminated steel	Hold field winding; spread flux evenly in the air gap
Field winding	Copper	Produces the main magnetic flux Φ when excited by DC
Armature core	Laminated silicon steel (≈ 0.5 mm)	Houses armature conductors; laminated to reduce eddy-current loss
Armature winding	Copper (lap or wave)	Conductors in which EMF is induced / current flows
Commutator	Hard-drawn copper segments insulated by mica	Mechanical rectifier (generator) / inverter (motor)
Brushes	Carbon / graphite	Collect current from the rotating commutator

Lap winding (A = P parallel paths) suits high-current, low-voltage machines; wave winding (A = 2) suits high-voltage, low-current machines.

2. DC Generator: Working and Commutation (Animation)

When armature conductors rotate in the magnetic field, they cut flux and an EMF is induced (Faraday’s law); its direction follows Fleming’s right-hand rule. Each conductor passes alternately under N and S poles, so the EMF in a coil is alternating. The split-ring commutator rotates with the coil and reverses the coil’s connection to the brushes exactly when the coil EMF reverses — so the brushes always see the same polarity.

Animation 1 – Coil EMF is AC (grey); the commutator flips the connection every half-turn, giving unidirectional voltage at the brushes (green). Real machines use many coils, so the output ripple becomes very small.

3. EMF Equation of a DC Generator

Let P = number of poles, Φ = flux per pole (Wb), Z = total armature conductors, N = speed (rpm), A = number of parallel paths.

1. Flux cut by one conductor in one revolution = PΦ; time for one revolution = 60/N s.
2. Average EMF per conductor = PΦN/60.
3. Conductors in series per path = Z/A.

E_g = P Φ Z N / (60 A) volts (lap: A = P; wave: A = 2)

For a given machine, E ∝ ΦN. Terminal voltage of a generator: V = E_g − I_aR_a − brush drop.

4. DC Motor: Working, Back EMF and Torque

When current flows in armature conductors placed in a magnetic field, each experiences a force F = BIL (direction by Fleming’s left-hand rule), producing torque. The commutator keeps the torque in one direction.

As the armature rotates, its conductors also cut flux and generate an EMF that opposes the applied voltage (Lenz’s law) — the back (counter) EMF:

E_b = PΦZN/(60A), V = E_b + I_aR_a, I_a = (V − E_b)/R_a T_a = 0.159 PΦZ I_a / A N·m ⇒ T ∝ Φ I_a; N ∝ E_b / Φ

Back EMF makes the motor self-regulating: when load increases, speed falls slightly, E_b falls, I_a rises and produces the extra torque. Mechanical power developed = E_bI_a.

5. Types of DC Machines (by Excitation)

Type	Field connection	Key feature
Separately excited	Field from an independent DC source	Precise, independent control of flux
Permanent magnet	Magnets instead of field winding	Small motors (toys, wipers, fans)
Shunt	Field (many turns, thin wire) in parallel with armature	Nearly constant flux → nearly constant speed
Series	Field (few turns, thick wire) in series with armature	Φ ∝ Ia → T ∝ Ia², very high starting torque, speed varies widely
Compound	Both shunt and series fields (long-shunt or short-shunt; cumulative or differential)	Combines good starting torque with limited speed variation

6. Motor Characteristics and Applications

Motor	Speed vs load	Starting torque	Applications
Shunt	Almost constant (5–15 % drop)	Medium	Lathes, drilling machines, fans, blowers, conveyors
Series	Falls sharply with load; dangerously high at no load	Very high	Electric traction (trains, trams), cranes, hoists, starter motors
Cumulative compound	Moderate drop	High	Rolling mills, presses, shears, lifts

⚠ Never start a series motor without loadAt no load the armature current is small, so flux (∝ I_a) is very small and speed N ∝ E_b/Φ becomes dangerously high — the motor can run away and fly apart. Series motors are therefore coupled directly or through gears, never through belts.

7. Why a Starter Is Needed

At standstill, N = 0, so E_b = 0 and the starting current I_a = V/R_a. Because R_a is very small (often below 1 Ω), this current can be 10–20 times the rated value, damaging the commutator and windings. A starter inserts resistance in the armature circuit at start and cuts it out step by step as the motor speeds up and builds back EMF. 3-point starters (with no-volt release) suit shunt motors; 4-point starters are used when wide field control is needed.

8. Speed Control

• Flux (field) control: a rheostat in the shunt field reduces Φ → speed above base speed. Efficient and simple.
• Armature resistance control: resistance in series with armature → speed below base speed; wasteful.
• Armature voltage control: varying supply voltage (Ward-Leonard system, or modern thyristor/chopper drives) → smooth control over a wide range.

9. Losses and Efficiency

• Copper losses (variable): armature I_a²R_a, series field, brush contact loss; shunt field loss is nearly constant.
• Iron (core) losses (constant): hysteresis and eddy-current losses in the armature core.
• Mechanical losses (constant): friction and windage.
• Maximum efficiency occurs when variable loss = constant loss. Swinburne’s test (no-load) is used to find constant losses of shunt machines.

10. Solved Problems

Problem 1. A 4-pole DC generator has 500 armature conductors, flux 0.02 Wb per pole and runs at 1200 rpm. Find the EMF for (a) lap and (b) wave winding.

1. (a) Lap, A = 4: E = 4 × 0.02 × 500 × 1200 / (60 × 4) = 200 V
2. (b) Wave, A = 2: E = 48 000/120 = 400 V

Problem 2. A 220 V shunt motor has R_a = 0.5 Ω and takes an armature current of 20 A at full load. Find the back EMF, the starting current without a starter, and the starter resistance to limit starting current to twice full load.

1. E_b = 220 − 20 × 0.5 = 210 V
2. Starting current (E_b = 0) = 220/0.5 = 440 A (22 × rated!)
3. Total R for 40 A = 220/40 = 5.5 Ω ⇒ external starter resistance = 5 Ω

Problem 3. The motor above runs at 1000 rpm with E_b = 210 V. If flux is reduced by 10 % and E_b stays about 210 V, find the new speed. N ∝ E_b/Φ ⇒ N₂ = 1000/0.9 ≈ 1111 rpm.

11. Practice MCQs (click to see answer)

1. The function of the commutator in a DC generator is to: (a) Increase voltage (b) Convert AC in the armature to DC at the brushes (c) Reduce sparking (d) Produce flux

✔ (b) Convert AC to DC (mechanical rectifier).

2. The EMF equation of a DC generator is: (a) E = PΦZN/60A (b) E = 4.44fNΦ (c) E = ΦZN/P (d) E = PΦN/60

✔ (a) E = PΦZN/60A.

3. For a wave-wound armature, the number of parallel paths is: (a) P (b) 2 (c) 2P (d) P/2

✔ (b) 2.

4. Which DC motor should never be started without load? (a) Shunt (b) Series (c) Cumulative compound (d) Separately excited

✔ (b) Series motor.

5. Back EMF in a DC motor is: (a) Equal to supply voltage (b) Always zero (c) Opposite to applied voltage (d) In phase with field current

✔ (c) Opposes the applied voltage.

6. A starter is used with a DC motor because at start: (a) Back EMF is zero (b) Flux is maximum (c) Speed is maximum (d) Field is open

✔ (a) Back EMF is zero, so current would be V/R_a.

7. The speed of a DC motor is: (a) Directly proportional to flux (b) Inversely proportional to flux (c) Independent of flux (d) Proportional to armature resistance

✔ (b) Inversely proportional to flux (N ∝ E_b/Φ).

8. Electric traction mostly used: (a) DC shunt motors (b) DC series motors (c) Synchronous motors (d) Stepper motors

✔ (b) DC series motors (historically), for high starting torque.

9. Field control of a shunt motor gives speeds: (a) Below base speed (b) Above base speed (c) Only zero speed (d) Fixed speed

✔ (b) Above base speed.

10. Brushes of DC machines are usually made of: (a) Copper (b) Carbon (c) Aluminium (d) Iron

✔ (b) Carbon/graphite.

11. Torque of a DC series motor before saturation is proportional to: (a) I_a (b) I_a² (c) 1/I_a (d) √I_a

✔ (b) I_a² (since Φ ∝ I_a).

12. বাংলায় দ্রুত রিভিশন

📝 পরীক্ষার আগে এক নজরে

• একই DC মেশিন জেনারেটর (ফ্লেমিংয়ের ডান হাত নিয়ম) ও মোটর (বাম হাত নিয়ম) হিসেবে কাজ করতে পারে।
• আর্মেচার কয়েলে AC আবিষ্ট হয়; কমিউটেটর ব্রাশে তা DC-তে রূপান্তর করে।
• EMF সমীকরণ: E = PΦZN/60A; ল্যাপ উইন্ডিংয়ে A = P, ওয়েভ উইন্ডিংয়ে A = 2।
• মোটরে ব্যাক EMF E_b = V − I_aR_a; গতি N ∝ E_b/Φ, টর্ক T ∝ ΦI_a।
• সিরিজ মোটরের শুরুর টর্ক খুব বেশি (ট্র্যাকশন, ক্রেন), কিন্তু লোড ছাড়া চালু করা যাবে না। শান্ট মোটর প্রায় স্থির গতিতে চলে (লেদ, ফ্যান)।
• শুরুতে E_b = 0, তাই কারেন্ট সীমিত রাখতে স্টার্টার লাগে।

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References: B. L. Theraja, Electrical Technology Vol. II; P. S. Bimbhra, Electrical Machinery; Chapman, Electric Machinery Fundamentals. Images and animations: original work by Totalecer.