A balanced 3-phase induction motor runs at slip s. If ωₛ is its synchronous speed, what is the relative speed between the stator MMF and rotor MMF?

1️⃣ sωₛ
2️⃣ (1 − s)ωₛ
3️⃣ ωₛ
4️⃣ zero

---

✅ Answer (Detailed Solution Below)

✔️ Option 4: zero

---

📖 Detailed Solution

🔷 Step 1: Speed of Stator MMF

When a balanced 3-phase supply is applied:

✔️ Stator produces a rotating magnetic field (MMF)
✔️ This rotates at synchronous speed ωₛ
✔️ This is with respect to stationary stator

So,

$$\text{Speed of Stator MMF}={\omega }_s$$

---

🔷 Step 2: Rotor Mechanical Speed

Rotor runs at slip s, therefore:

$${\omega }_r=(1-s){\omega }_s$$

---

🔷 Step 3: Rotor MMF Speed Relative to Rotor

Rotor current frequency:

$$f_r=sf$$

Rotor MMF rotates at slip speed relative to rotor:

$$\text{Rotor MMF speed (w.r.t rotor)}=s{\omega }_s$$

---

🔷 Step 4: Rotor MMF Speed Relative to Stator

To find rotor MMF speed with respect to stator:

$$\text{Rotor MMF speed (w.r.t stator)}=\text{Rotor mechanical speed}+\text{Rotor MMF speed (w.r.t rotor)}$$$$=(1-s){\omega }_s+s{\omega }_s$$$$={\omega }_s$$

---

🎯 Final Result

✔ Stator MMF rotates at ωₛ
✔ Rotor MMF also rotates at ωₛ

Therefore,

$$\text{Relative speed}={\omega }_s-{\omega }_s=0$$

---

⭐ Important Physical Meaning

✔ Stator field and rotor field rotate together
✔ They are stationary relative to each other
✔ This ensures steady electromagnetic torque
✔ If relative speed existed → torque would pulsate

---

❌ Why Other Options Are Incorrect

❌ 1️⃣ sωₛ

This is rotor MMF speed relative to rotor, not relative to stator MMF.

❌ 2️⃣ (1 − s)ωₛ

This is rotor mechanical speed.

❌ 3️⃣ ωₛ

This is speed relative to stationary stator, not relative to stator MMF.

---

📌 Key One-Line Exam Statement ⭐

In a 3-phase induction motor, both stator MMF and rotor MMF rotate at synchronous speed; hence their relative speed is zero.

---

📝 Final Conclusion

Although rotor mechanically runs at (1 − s)ωₛ, the rotor MMF rotates at synchronous speed relative to stator.

$$\boxed{{\displaystyle \text{Relative speed between stator MMF and rotor MMF = 0}}}$$

👉 Correct Answer: Option 4 (zero)