📘 Induction Motor – Very Hard Multi-Step Problems
These problems combine multiple concepts. Solve step by step carefully.
🔹 Problem 1 – Power Flow + Torque + Slip
A 4-pole, 50 Hz induction motor runs at 1440 rpm. Rotor input power = 6000 W. Mechanical losses = 200 W. Find: 1) Slip 2) Rotor copper loss 3) Output torque Step 1: Synchronous speed Ns = 120f / P = 120 × 50 / 4 = 1500 rpm Step 2: Slip s = (1500 − 1440)/1500 = 60/1500 s = 0.04 Step 3: Rotor copper loss = s × Rotor input = 0.04 × 6000 = 240 W Step 4: Mechanical power developed = (1 − s) × Rotor input = 0.96 × 6000 = 5760 W Step 5: Output power = 5760 − 200 = 5560 W Step 6: Torque T = (9550 × P(kW)) / N = (9550 × 5.56) / 1440 T ≈ 36.8 Nm🔹 Problem 2 – Rotor Resistance Change
An induction motor develops maximum torque at 10% slip. Find ratio R2/X2. Condition: s_max = R2 / X2 Given s_max = 0.1 Therefore: R2 / X2 = 0.1 If rotor resistance doubled: New slip for maximum torque: = 2R2 / X2 = 2 × 0.1 = 0.2 New slip = 20% Important conclusion: Increasing rotor resistance increases slip at maximum torque, but maximum torque value remains same.🔹 Problem 3 – Starting Torque Comparison
Given: R2 = 0.5 Ω X2 = 2 Ω Starting slip = 1 Torque proportional to: T ∝ sR2 / (R2² + (sX2)²) At starting: T_start ∝ 1×0.5 / (0.25 + 4) = 0.5 / 4.25 = 0.1176 At maximum torque: s_max = R2/X2 = 0.5/2 = 0.25 T_max ∝ 0.25×0.5 / (0.25 + (0.5)²) = 0.125 / (0.25 + 0.25) = 0.125 / 0.5 = 0.25 Therefore: T_start / T_max = 0.1176 / 0.25 ≈ 0.47 Starting torque ≈ 47% of maximum torque.🔹 Problem 4 – Speed After Load Change
At full load: Slip = 4% Load torque reduced by 50%. Since near synchronous speed: Torque ∝ slip New slip ≈ 2% New speed: Nr = Ns(1 − s) = 1500 × (0.98) = 1470 rpm Motor speed increases.🔹 Advanced Observations
- Rotor copper loss directly proportional to slip
- Maximum torque independent of rotor resistance
- Speed change small due to small slip variation
- Torque proportional to slip near synchronous speed
🎯 Hard-Level GATE Focus
- Multi-step power flow questions
- Effect of rotor resistance change
- Torque ratio problems
- Slip-based reasoning questions
Induction Motor Advanced Numericals = Concept Mastery Zone
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