A three-phase 6-pole, 50 Hz induction motor is running at 5% slip. What is the speed of the motor?

1️⃣ 850 rpm
2️⃣ 900 rpm
3️⃣ 950 rpm
4️⃣ 1,000 rpm

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✅ Answer (Detailed Solution Below)

✔️ Option 3: 950 rpm

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📖 Detailed Solution

🔷 Concept of Induction Motor Speed

In a 3-phase induction motor:

✔️ The stator is stationary
✔️ The stator magnetic field rotates at synchronous speed (Ns)
✔️ The rotor rotates at a speed slightly less than Ns
✔️ The difference is called slip

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🔷 Step 1: Calculate Synchronous Speed

Formula:

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

Where:
➤ f = 50 Hz
➤ P = 6 poles

$$N_s=\frac{120\times 50}{6}$$$$N_s=1000\text{ rpm}$$

✔️ Synchronous Speed = 1000 rpm

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🔷 Step 2: Calculate Rotor Speed Using Slip

Slip formula:

$$s=\frac{N_s-N_r}{N_s}$$

Rearranging:

$$N_r=N_s(1-s)$$

Given:

$$s=5\mathrm{\%}=0.05$$$$N_r=1000(1-0.05)$$$$N_r=1000\times 0.95$$$$N_r=950\text{ rpm}$$

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🎯 Final Motor Speed = 950 rpm

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🔎 Additional Important Understanding

✔ Speed of stator magnetic field = 1000 rpm
✔ Speed of rotor magnetic field = 1000 rpm
✔ Relative speed between stator & rotor fields = 0

Slip speed:

$$SlipSpeed=N_s-N_r$$$$=1000-950=50\text{ rpm}$$

✔ Rotor rotates 50 rpm slower than rotating magnetic field

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❌ Why Other Options Are Incorrect

❌ 1️⃣ 850 rpm

This corresponds to 15% slip, not 5%.

❌ 2️⃣ 900 rpm

This corresponds to 10% slip.

❌ 4️⃣ 1,000 rpm

This is synchronous speed.
Rotor can never reach Ns in induction motor.

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⭐ Important Exam Points

✔ Rotor speed is always less than synchronous speed
✔ Slip must exist for torque production
✔ Ns depends only on frequency and poles
✔ Rotor speed depends on slip

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📌 Key One-Line Exam Statement ⭐

For a 6-pole, 50 Hz induction motor running at 5% slip, the rotor speed is 950 rpm.

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📝 Final Conclusion

The synchronous speed of the motor is 1000 rpm.
With 5% slip, the actual rotor speed becomes:

$$\boxed{{\displaystyle 950\text{ rpm}}}$$

👉 Correct Answer: Option 3 (950 rpm)