The relative speed between stator and rotor fluxes is equal to __________.

1️⃣ Synchronous speed, $N_s$
2️⃣ Rotor speed, $N$
3️⃣ Zero
4️⃣ $N_s-N$

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✅ Answer (Detailed Solution Below)

✔️ Option 3: Zero

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📖 Detailed Solution

🔹 In a 3-phase induction motor, two main magnetic fields are produced:

✔️ Stator magnetic field
✔️ Rotor magnetic field

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⚙️ Speed of Magnetic Fields

🔹 Stator Flux Speed

🔹 When 3-phase AC is applied:

✔️ A rotating magnetic field is produced.
✔️ It rotates at synchronous speed:

$$$$Ns=120fP

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🔹 Rotor Flux Speed

🔹 Rotor current is induced due to relative motion.
🔹 Rotor current produces rotor flux.
🔹 Rotor flux rotates at:

✔️ Slip speed with respect to rotor
✔️ But synchronous speed with respect to stator

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🔹 Important Result

👉 Both stator flux and rotor flux rotate at synchronous speed with respect to stator.

$$$$Speed of stator flux=Ns$$$$Speed of rotor flux=Ns

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🔹 Relative Speed Between Fluxes

$$$$Relative Speed=Ns−Ns=0

👉 Hence, relative speed = Zero

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📐 Why This Happens

🔹 Rotor speed = $N$ (less than $N_s$)
🔹 Slip = $s=\frac{N_s-N}{N_s}$

🔹 Rotor flux rotates at slip speed relative to rotor:

$$$$Rotor flux speed (w.r.t rotor)=sNs

🔹 Rotor speed = $(1-s)N_s$

🔹 Therefore, rotor flux speed w.r.t stator:

$$$$(1−s)Ns+sNs=Ns

👉 Rotor flux also rotates at synchronous speed.

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❌ Why Other Options are Incorrect

(1) Synchronous Speed, $N_s$ ❌

🔹 This is speed of flux, not relative speed.

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(2) Rotor Speed, $N$ ❌

🔹 Rotor speed is mechanical speed, not flux speed.

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(4) $N_s-N$ ❌

🔹 This is slip speed between stator field and rotor, not between fluxes.

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📘 Important Relationships

Quantity	Speed
Stator Flux	$N_s$
Rotor Flux	$N_s$
Rotor	$N<N_s$
Slip Speed	$N_s-N$
Relative Speed (Fluxes)	0

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📌 Comparison with Other Machines

Induction Motor

✔️ Stator & Rotor Flux → Same speed
✔️ Relative speed = 0

Synchronous Motor

✔️ Field & Armature Flux → Same speed
✔️ Relative speed = 0

DC Motor

✔️ Field & Armature Flux → Same speed
✔️ Relative speed = 0

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⭐ Important Exam Points

✔️ Both fluxes rotate at Ns
✔️ Rotor speed < Ns
✔️ Slip exists
✔️ Flux relative speed = 0

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📌 Key One-Line Exam Statement ⭐

In an induction motor, both stator and rotor magnetic fields rotate at synchronous speed, so their relative speed is zero.

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📝 Final Conclusion

📍 In a 3-phase induction motor, the rotor flux and stator flux rotate at the same synchronous speed with respect to stator. Therefore, the relative speed between them is zero.

👉 Hence, Option 3 is Correct.