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DC Machines & Induction Motors
Torque-speed curves, starters, slip and V/f control — the rotating-machine half of every EEE technical round.
BHELSiemensABBSchneider ElectricL&T Electrical
Key formulas
s = (Ns − N) / Ns; Ns = 120·f / P
Slip: Synchronous speed depends on supply frequency and pole pairs; a 4-pole 50 Hz motor has Ns = 1500 rpm.
T = (3 / ωs) · s·E₂²·R₂ / (R₂² + (s·X₂)²)
Induction motor torque: Shows why torque rises with slip up to a point, then falls when sX₂ dominates.
N ∝ (V − Ia·Ra) / Φ
DC motor speed: Base of all DC speed-control questions: armature-voltage control, field weakening, armature resistance.
Cheat sheet
- ▸DC motor: back EMF Eb = kΦω; speed N ∝ (V − Ia·Ra)/Φ. Series motors have huge starting torque and must never run unloaded; shunt motors run at nearly constant speed.
- ▸3-phase induction motor runs below synchronous speed — slip s = (Ns − N)/Ns. At standstill s = 1, at synchronous speed s = 0 (zero torque).
- ▸Torque ∝ s·E²·R2 / (R2² + (s·X2)²). Starting torque rises with rotor resistance; max torque is independent of R2 but occurs at higher slip.
- ▸Starters: stator resistance/star-delta/autotransformer for squirrel-cage motors; rotor resistance starter only for slip-ring motors. DC motors need starting resistance to limit armature current (no back-EMF at standstill).
- ▸V/f control keeps air-gap flux constant: speed is controlled by varying supply frequency together with voltage — the basis of every modern VFD/inverter drive.
- ▸Squirrel-cage rotor: rugged, low maintenance, low starting torque. Slip-ring: external resistance can be added, high starting torque, needs maintenance.
Squirrel-cage vs Slip-ring induction motor
| Aspect | Squirrel cage | Slip ring (wound rotor) |
|---|---|---|
| Rotor | Bars shorted by end rings | 3-phase winding + slip rings |
| Starting torque | Low–moderate | High (external rotor resistance) |
| Starting current | 5–7 × full load (needs starter) | Lower with rotor resistance |
| Maintenance | Almost none | Brushes and rings need service |
| Cost / use | Cheap, standard industrial drive | Cranes, hoists, high-inertia loads |
Visual
Torque–slip curve (induction motor):
T
| ___---‾‾
| __/ \___
| __/ \___ (stable region → unstable)
+--|----|-------|-----|---- s
0 smax 1.0 (standstill)
Torque peaks at smax = R2/X2 and is independent of R2.Top 4 campus interview questions
MCQ mastery quiz
1. A 4-pole, 50 Hz induction motor runs at 1440 rpm. Its slip is…
2. A DC series motor should never be started…
3. Maximum torque of an induction motor is independent of…
4. V/f control is used in VFDs primarily to…