Why this topic is important for ECET?
Synchronous motors are a vital part of ECET syllabus under AC Machines. V-curves of synchronous motors help in analyzing the relation between armature current and field excitation, which is frequently asked in ECET as both theory and numerical. Mastering this ensures you can handle machine performance questions quickly in the exam.
📘 Concept Notes
1. Synchronous Motor Basics
- A synchronous motor runs at synchronous speed:
where
= frequency (Hz), 
= number of poles. - Unlike induction motors, synchronous motors are not self-starting; they need auxiliary means for starting (pony motor or damper windings).
- They can operate at lagging, unity, or leading power factor depending on excitation.
2. Excitation and Armature Current Relationship
- The motor has two controls:
- Field excitation (DC) → controls motor’s power factor.
- Load torque → controls active power drawn.
- If excitation is:
- Normal excitation: Motor operates at unity power factor.
- Under-excitation: Motor draws lagging current.
- Over-excitation: Motor draws leading current (used for power factor correction).
3. V-Curves of Synchronous Motor
- A V-curve is a plot of armature current (Ia) versus field excitation (If) at constant load.
- Shape: The curve looks like the English alphabet “V”.
- At low excitation → high lagging current.
- At correct excitation → minimum current at unity power factor.
- At high excitation → high leading current.
Inverted V-curves: Plot of power factor vs field current.
4. Applications of V-Curves
- Determining the operating condition of synchronous motor.
- Used for power factor correction in industries.
- Helpful in deciding excitation control strategy.
Example:
A synchronous motor supplying constant mechanical load shows:
- At 0.8 under-excited → lagging PF.
- At unity excitation → unity PF.
- At 1.2 over-excited → leading PF.
⚙️ Formulas
- Synchronous speed:
Power input to motor:
Armature current relation:
Power factor angle:
Maximum power:
🔟 10 MCQs
Q1. The synchronous speed of a 4-pole motor at 50 Hz is:
a) 750 rpm
b) 1500 rpm
c) 3000 rpm
d) 1000 rpm
Q2. A synchronous motor at unity power factor operates at:
a) Normal excitation
b) Under-excitation
c) Over-excitation
d) None
Q3. In V-curves, the minimum armature current occurs at:
a) Lagging PF
b) Unity PF
c) Leading PF
d) Zero PF
Q4. Over-excited synchronous motor draws:
a) Lagging current
b) Leading current
c) Zero current
d) None
Q5. The shape of the V-curve is:
a) Parabolic
b) Hyperbolic
c) V-shaped
d) Circular
Q6. A 6-pole synchronous motor runs at 1000 rpm. Find supply frequency.
a) 25 Hz
b) 50 Hz
c) 60 Hz
d) 75 Hz
Q7. For a synchronous motor, power developed is maximum when:
a) δ = 0°
b) δ = 90°
c) δ = 180°
d) δ = 45°
Q8. If field excitation is reduced, the motor tends to draw:
a) More lagging current
b) More leading current
c) Zero current
d) None
Q9. Which theorem explains V-curves?
a) Thevenin’s theorem
b) Maximum power transfer theorem
c) Phasor diagram of synchronous motor
d) Superposition theorem
Q10. Synchronous motors are used for:
a) Variable speed applications
b) Constant speed applications
c) High starting torque applications
d) None
✅ Answer Key
| Q.No | Answer |
|---|---|
| 1 | b |
| 2 | a |
| 3 | b |
| 4 | b |
| 5 | c |
| 6 | b |
| 7 | b |
| 8 | a |
| 9 | c |
| 10 | b |
🧠 Explanations
- Q1:
→ (b). - Q2: Unity PF occurs at normal excitation → (a).
- Q3: At unity PF, current is minimum → (b).
- Q4: Over-excited motor → leading current → (b).
- Q5: By definition, curve is V-shaped → (c).
- Q6:
→ (b). - Q7: Maximum power when
→ (b). - Q8: Lower excitation → lagging PF → (a).
- Q9: Explained by phasor diagram → (c).
- Q10: Synchronous motors → constant speed → (b).
🎯 Motivation / Why Practice Matters
For ECET 2026, questions on synchronous motors and V-curves are sure-shot scoring because they are formula-based + concept-based. With daily practice, you can quickly identify PF conditions, excitation levels, and solve numericals in under 30 seconds. Mastering this gives you a competitive edge in machine-related problems.
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