The rotor of a three-phase, 5 kW, 400 V, 50 Hz, slip-ring induction motor is wound for 6 poles while its stator is wound for 4 poles. The approximate no-load steady-state speed when connected to 400 V, 50 Hz supply is

A) 1500 rpm
B) 500 rpm
C) 0 rpm
D) 1000 rpm

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✅ Answer:

➡️ C) 0 rpm

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🧠 Detailed Solution

◆ Step 1: Core Concept

→ Stator produces rotating magnetic field (RMF)
→ Rotor can follow RMF only if pole configuration matches

➡️ Condition for torque:
Stator poles = Rotor poles

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◆ Step 2: Given Data

→ Stator poles $P_s=4$
→ Rotor poles $P_r=6$
→ Frequency $f=50Hz$

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◆ Step 3: Synchronous Speed

$N_s=\frac{120f}{P}$

$${\mathrm{<span\; style="font-size:\; medium;">N</span>}}_{\mathrm{<span\; style="font-size:\; medium;">s</span>}}<span\; style="font-size:\; medium;">=</span>\frac{\mathrm{<span\; style="font-size:\; medium;">120</span>}<span\; style="font-size:\; medium;">\times </span>\mathrm{<span\; style="font-size:\; medium;">50</span>}}{\mathrm{<span\; style="font-size:\; medium;">4</span>}}<span\; style="font-size:\; medium;">=</span>\mathrm{<span\; style="font-size:\; medium;">1500</span>}\text{<span style="font-size: medium;">\hspace{0.17em}</span>}\text{<span style="font-size: medium;">rpm</span>}$$

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◆ Step 4: Key Technical Insight 🚨

→ Stator creates 4-pole RMF
→ Rotor is designed for 6 poles

➡️ Magnetic fields do NOT align
➡️ No electromagnetic coupling

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◆ Step 5: Result

→ No coupling ⇒ No torque
→ No torque ⇒ No rotation

➡️ Final Speed = 0 rpm

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❌ Why Other Options Are Incorrect

◆ A) 1500 rpm → Requires same poles
◆ B) 500 rpm → No such operating condition
◆ D) 1000 rpm → Not applicable

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🔑 Key Points to Remember

◆ Torque requires equal pole numbers
◆ Pole mismatch ⇒ No magnetic interaction
◆ No interaction ⇒ No torque ⇒ No rotation
◆ Very common exam trap

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🎯 Final Conclusion

➡️ Due to mismatch of poles (4 vs 6):

Motor cannot develop torque ⇒ Speed = 0 rpm