GATE Electrical Engineering - Complete Master Library

 

📘 Induction Motor – Torque Slip Characteristics

Torque-slip curve explains starting torque, maximum torque and operating region of induction motor. Very important for GATE.

---

🔹 1. Torque Equation

From equivalent circuit:

T ∝ (s E₂² R₂') / [ (R₂'/s)² + X₂'² ]

Key observation: Torque depends on slip.

---

🔹 2. Important Regions

1️⃣ Starting (s = 1) 2️⃣ Normal operation (s small, 2–5%) 3️⃣ Maximum torque (pull-out torque)

---

🔹 3. Starting Torque

At s = 1:

T_start ∝ (E₂² R₂') / (R₂'² + X₂'²)

Important concept: Increasing rotor resistance increases starting torque.

---

🔹 4. Maximum Torque Condition

Maximum torque occurs when:

R₂'/s = X₂'

Or,

s_max = R₂' / X₂'

Very important result.

---

🔹 5. Important Result

Maximum torque is independent of rotor resistance. Changing R₂' shifts the slip at which maximum torque occurs.

---

🔹 6. Example

Given: R₂' = 0.4 Ω X₂' = 2 Ω Find slip at maximum torque. Solution:

s_max = R₂' / X₂' = 0.4 / 2 = 0.2

Maximum torque occurs at 20% slip.

---

🔹 7. Torque-Slip Curve Shape

• Linear region at small slip
• Peak at maximum torque
• Decreases at high slip

Stable region: Small slip region.

---

🎯 GATE Important Points

• Remember s_max formula clearly
• Maximum torque independent of R₂'
• Starting torque affected by R₂'
• Motor operates in low slip region

Torque ∝ Slip (for small slip) Maximum Torque when R₂'/s = X₂'