A) 120 Hz, 60 Hz
B) 90 Hz, 210 Hz
C) 186 Hz, 86 Hz
D) 180 Hz, 210 Hz
✅ Answer:
➡️ B) 90 Hz, 210 Hz
🧠Detailed Solution
◆ Step 1: Synchronous Speed of Stator Field
N_s = \frac{120 f}{P}
N_s = \frac{120 \times 60}{6} = 1200 \, \text{rpm}
◆ Step 2: Mechanical Frequency of Rotor
f_m = \frac{P \times N}{120} = \frac{6 \times 3000}{120} = 150 \, \text{Hz}
◆ Step 3: Key Concept (Very Important 🚨)
➡️ Output frequency depends on relative speed between RMF and rotor
Two cases:
◆ Case 1: Opposite Direction
→ Relative speed increases
f_2 = f_m + f_1 = 150 + 60 = 210 \, \text{Hz}
◆ Case 2: Same Direction
→ Relative speed decreases
f_2 = f_m - f_1 = 150 - 60 = 90 \, \text{Hz}
❌ Why Other Options Are Incorrect
◆ A) 120, 60 → Not derived from relative speed
◆ C) 186, 86 → No valid calculation
◆ D) 180, 210 → 180 Hz is incorrect assumption
🔑 Key Points to Remember
◆ Induction frequency converter works on relative motion principle
◆ Output frequency = sum or difference of frequencies
◆ Mechanical frequency:
◆ Two outputs always possible → (f_m ± f_1)
🎯 Final Conclusion
➡️ Possible output frequencies are:
90 Hz and 210 Hz ✔️