A) f₁ = s f₂
B) f₂ = s f₁
C) f₂ = f₁ (1 − s)
D) f₂ = √(s f₁)
✅ Answer: B) f₂ = s f₁
đ§ Detailed Solution:
◆ Step 1: Fundamental Concept
In an induction motor:
→ Stator is supplied with frequency f₁
→ Rotor frequency depends on slip (relative motion)
◆ Step 2: Definition of Slip
s = (Ns − Nr) / Ns
◆ Step 3: Speed-Frequency Relation
N = (120 × f) / P
◆ Step 4: Rotor Frequency Derivation
Rotor frequency depends on slip speed:
f₂ = (Slip speed / Synchronous speed) × f₁
Since (Slip speed / Synchronous speed) = s:
f₂ = s f₁
◆ Step 5: Special Cases
→ At standstill: s = 1 → f₂ = f₁
→ At synchronous speed: s = 0 → f₂ = 0
→ Normal operation: s small → f₂ small
❌ Why Other Options Are Incorrect
A) f₁ = s f₂ → Incorrect relation
C) f₂ = f₁ (1 − s) → Not applicable
D) √(s f₁) → Invalid expression
đ Key Points
◆ Rotor frequency depends on slip
◆ Formula: f₂ = s f₁
◆ At standstill → rotor frequency = supply frequency
◆ At synchronous speed → rotor frequency = zero
đŻ Final Conclusion
Relationship between rotor frequency, slip, and stator frequency = f₂ = s f₁