A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor operates at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, as seen by a stationary observer, is:

A) 1500
B) 1470
C) 157
D) 154

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✅ Answer:

➡️ C) 157 rad/sec

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🧠 Detailed Solution

◆ Step 1: Key Concept (Very Important 🚨)

➡️ Rotor flux rotates at synchronous speed, not rotor speed

→ Even though rotor rotates slower,
→ Rotor magnetic field rotates at synchronous speed (Ns)

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◆ Step 2: Calculate Synchronous Speed

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

$$N_s=\frac{120\times 50}{4}=1500\text{rpm}$$

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◆ Step 3: Convert to Angular Speed

$${\omega }_s=\frac{2\pi N_s}{60}$$$${\omega }_s=\frac{2\pi \times 1500}{60}=157\text{rad/sec}$$

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◆ Step 4: Important Insight

➡️ Rotor speed ≠ Rotor flux speed
➡️ Rotor flux speed = Synchronous speed

➡️ Slip does NOT affect rotor flux speed

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❌ Why Other Options Are Incorrect

◆ A) 1500 → rpm, not rad/sec
◆ B) 1470 → Rotor speed (approx), not flux speed
◆ D) 154 → Incorrect calculation

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🔑 Key Points to Remember

◆ Rotor flux always rotates at synchronous speed
◆ Slip affects rotor speed, not flux speed
◆ Convert rpm → rad/sec using $\omega =\frac{2\pi N}{60}$
◆ Very common conceptual + numerical question

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🎯 Final Conclusion

➡️ Speed of rotor flux =

157 rad/sec ✔️