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ECET 2026 EEE

Day 6 ECET 2026 Night – DC Machines: DC Motors (Types & Torque Equation)

Concept Notes

1. DC Motor Basics

A DC motor converts electrical energy into mechanical energy using the principle:

When a current-carrying conductor is placed in a magnetic field, it experiences a force (Lorentz Force).


2. Types of DC Motors

(a) Shunt Motor

  • Field winding in parallel with armature.
  • Constant speed, good for lathes, fans.
  • Torque is moderate.

(b) Series Motor

  • Field winding in series with armature.
  • Very high starting torque.
  • Speed varies widely with load.
  • Used in cranes, traction, elevators.

(c) Compound Motor

  • Combination of series + shunt field.
  • Cumulative compound: High starting torque + better speed regulation.
  • Differential compound: Rarely used.

(d) Permanent Magnet DC Motor (PMDC)

  • Uses permanent magnets for field.
  • Compact, efficient, widely used in toys, EVs, robotics.

3. Torque in DC Motors

The force on a conductor:

 F = B \cdot I \cdot l

Torque:

 T = F \cdot r

For a motor with  Z conductors,  P poles, flux per pole  \phi , and armature current  I_a :

 T = \frac{P \cdot Z}{2 \pi \cdot A} \cdot \phi \cdot I_a

Where:

  •  A = number of parallel paths
  •  \phi = flux per pole
  •  I_a = armature current

Simplified:

 T \propto \phi \cdot I_a


4. Speed Equation of DC Motor

Back emf:

 E_b = \frac{P \phi Z N}{60 A}

Voltage equation:

 V = E_b + I_a R_a

So,

 N \propto \frac{V - I_a R_a}{\phi}

  • Shunt motor → Speed almost constant (since  \phi is constant).
  • Series motor → Speed varies widely with load.

⚙️ Formulas

  • Force on conductor:  F = B I l
  • Torque:  T = F r
  • General torque eqn:  T = \frac{P Z}{2 \pi A} \phi I_a
  • Proportional torque:  T \propto \phi I_a
  • Back emf:  E_b = \frac{P \phi Z N}{60 A}
  • Motor equation:  V = E_b + I_a R_a
  • Speed:  N \propto \frac{V - I_a R_a}{\phi}

🔟 10 MCQs

Q1. The basic principle of DC motor operation is:
a) Lenz’s law
b) Faraday’s law
c) Lorentz force law
d) Ampere’s circuital law

Q2. Which DC motor has nearly constant speed under varying load?
a) Series
b) Shunt
c) Compound
d) PMDC

Q3. A series motor is preferred for:
a) Fans
b) Lathes
c) Electric traction
d) Measuring instruments

Q4. The torque of a DC motor is directly proportional to:
a)  I_a^2
b)  \phi I_a
c)  \phi^2
d) None

Q5. The speed of a DC motor is given by:
a)  N \propto \frac{V}{\phi}
b)  N \propto \frac{V - I_a R_a}{\phi}
c)  N \propto V \cdot \phi
d)  N \propto I_a

Q6. In a DC shunt motor, if flux reduces by 10% (constant V), speed will:
a) Remain same
b) Increase
c) Decrease
d) Zero

Q7. For maximum torque in a DC motor:
a)  \phi = 0
b)  I_a = 0
c) Both high
d) Both low

Q8. Which motor is best suited for elevators?
a) Shunt
b) Series
c) Compound
d) PMDC

Q9. If back emf equals supply voltage in a DC motor:
a) Motor runs normally
b) Motor stops
c) Armature current becomes zero
d) Both b and c

Q10. The starting torque of a DC series motor is:
a) Low
b) Medium
c) High
d) Negligible


✅ Answer Key

Q.NoAnswer
1c
2b
3c
4b
5b
6b
7c
8b
9c
10c

🧠 Explanations

  • Q1: Motor works on Lorentz force principle → (c).
  • Q2: Shunt motor → nearly constant speed → (b).
  • Q3: Series motor → high starting torque → traction → (c).
  • Q4: From torque eqn →  T \propto \phi I_a → (b).
  • Q5:  N \propto \frac{V - I_a R_a}{\phi} → (b).
  • Q6: If flux decreases → speed increases → (b).
  • Q7: Torque is maximum when both  \phi and  I_a are large → (c).
  • Q8: Elevators need high starting torque → series motor → (b).
  • Q9: If  E_b = V , then  I_a = 0 → motor stops → (c).
  • Q10: Series motor → very high starting torque → (c).

🎯 Motivation / Why Practice Matters

DC motors form the heart of many electrical machines. Questions on torque equation, speed control, and motor types are guaranteed in ECET 2026. Practicing ensures you can quickly distinguish motor characteristics and solve numerical torque/speed problems confidently.


📲 CTA

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