📘 Single Phase Induction Motor – Advanced Numerical Problems
Advanced problems based on double revolving field theory. Very important for conceptual clarity.
🔹 Problem 1 – Torque Ratio (Forward vs Backward)
Given: Slip s = 0.05 Rotor resistance R2 = 0.5 Ω Rotor reactance X2 = 2 Ω Torque proportional to: T ∝ (sE²R2) / (R2² + (sX2)²) Forward slip = s = 0.05 Backward slip = 2 − s = 1.95 Compare torque ratio Tf / Tb. For forward field: Denominator = (0.5)² + (0.05×2)² = 0.25 + (0.1)² = 0.25 + 0.01 = 0.26 For backward field: Denominator = (0.5)² + (1.95×2)² = 0.25 + (3.9)² = 0.25 + 15.21 = 15.46 Since backward denominator much larger,Forward torque >> Backward torque
Therefore motor produces net torque.🔹 Problem 2 – Starting Condition
At starting: s = 1 Backward slip: s_b = 2 − 1 = 1 Forward and backward slips equal. Therefore: Tf = TbNet starting torque = 0
Explains why motor is not self-starting.🔹 Problem 3 – Rotor Copper Loss Distribution
Given: Total rotor input = 800 W Slip = 0.04 Rotor copper loss: = s × Rotor input = 0.04 × 800Rotor copper loss = 32 W
Mechanical power: = (1 − s) × 800 = 0.96 × 800Mechanical power = 768 W
🔹 Problem 4 – Efficiency Calculation
Given: Mechanical output = 700 W Input power = 900 W Efficiency: η = Output / Input = 700 / 900η ≈ 77.8%
🔹 Problem 5 – Speed at Given Slip
Given: f = 50 Hz P = 6 poles Slip = 0.03 Ns = 120f / P = 120 × 50 / 6 = 1000 rpm Actual speed: Nr = Ns(1 − s) = 1000 × (0.97)Nr = 970 rpm
🔹 Key Advanced Observations
- Backward slip always near 2 at low slip
- Forward torque dominates in steady state
- At starting, both torques equal
- Double revolving field theory explains behavior clearly
🎯 GATE Hard-Level Points
- Backward slip formula very important
- Torque comparison concept frequently asked
- Slip-based power distribution questions common
- Understand denominator effect in torque equation
Single Phase IM = Two Motors in Opposite Directions
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