(Solved) A 4-pole induction motor, supplied by a slightly unbalanced 3-phase, 50 Hz source, runs at 1440 rpm. The electrical frequency of induced negative sequence rotor current is:

A) 100 Hz
B) 98 Hz
C) 52 Hz
D) 48 Hz

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✅ Answer:

➡️ B) 98 Hz

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🧠 Detailed Solution

◆ Step 1: Synchronous Speed

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

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

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◆ Step 2: Calculate Slip

$$s=\frac{N_s-N_r}{N_s}=\frac{1500-1440}{1500}=0.04$$

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◆ Step 3: Key Concept (Very Important 🚨)

➡️ For negative sequence currents:

$$f_2=(2-s)f$$

➡️ Reason:
→ Negative sequence field rotates opposite to rotor
→ Relative speed becomes (2 – s) times synchronous relation

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◆ Step 4: Calculate Frequency

$$f_2=(2-0.04)\times 50$$$$f_2=1.96\times 50=98\text{Hz}$$

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❌ Why Other Options Are Incorrect

◆ A) 100 Hz → Occurs if slip ≈ 0
◆ C) 52 Hz → From (1 + s)f, not applicable
◆ D) 48 Hz → From sf (positive sequence rotor freq)

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🔑 Key Points to Remember

◆ Positive sequence rotor frequency: $f_r=sf$
◆ Negative sequence rotor frequency: $f_2=(2-s)f$
◆ Negative sequence rotates opposite direction
◆ Produces double-frequency effect (~2f)

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🎯 Final Conclusion

➡️ Electrical frequency of negative sequence rotor current =
98 Hz ✔️