An induction motor develops maximum torque at slip = 0.2.1.If rotor resistance is doubled, slip at maximum torque increases.2.Maximum torque value remains unchanged with rotor resistance variation.3.Starting torque increases with rotor resistance.4.Maximum torque occurs at synchronous speed.Which of the above statements is/are correct?

Correct Answer: A - 1, 2 and 3 only

Quick Concept Explanation

The torque-slip curve changes shape when rotor resistance is changed. The given initial s_max=0.2 is not needed to prove the qualitative relationships. Doubling R2 doubles the approximate slip at maximum torque until model limits; Tmax remains unchanged. Key relation: Approximate condition: s_max ∝ R2/Xeq. At s=1, starting torque rises as rotor resistance is increased toward the optimum R2≈Xeq.

Exam focus: Rotor resistance shifts the torque-slip curve horizontally, not vertically at Tmax. Common trap: Saying maximum torque occurs at synchronous speed; torque is zero at s=0.

Statement-wise Verification

• Statement 1 - Correct.
  If rotor resistance is doubled, slip at maximum torque increases.
  S_max is proportional to rotor resistance, so increasing R2 shifts the peak torque to higher slip.
• Statement 2 - Correct.
  Maximum torque value remains unchanged with rotor resistance variation.
  Under constant supply and the standard equivalent-circuit approximation: the magnitude of maximum torque is essentially independent of rotor resistance.
• Statement 3 - Correct.
  Starting torque increases with rotor resistance.
  In the intended slip-ring-motor context: adding rotor resistance moves the operating point toward the condition for maximum starting torque and is the classic starting-torque improvement method (up to the optimum).
• Statement 4 - Incorrect.
  Maximum torque occurs at synchronous speed.
  At synchronous speed slip s=0, rotor induced emf/current and electromagnetic torque are zero.

Core Concept

The torque-slip curve changes shape when rotor resistance is changed. Maximum torque height remains nearly fixed, while its location moves because the condition R2/s ≈ Xeq is reached at a different slip. This is why external resistance is valuable for wound-rotor starting.

Formula / Key Relationship

Approximate condition: s_max ∝ R2/Xeq. At s=1, starting torque rises as rotor resistance is increased toward the optimum R2≈Xeq.

Step-by-Step Check

The given initial s_max=0.2 is not needed to prove the qualitative relationships. Doubling R2 doubles the approximate slip at maximum torque until model limits; Tmax remains unchanged. Therefore A.

Why the Other Options Are Wrong

Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.

Answer-Key Verification Note

The uploaded provisional key marks C . After independent technical verification, the defensible answer is A . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

Rotor resistance shifts the torque-slip curve horizontally, not vertically at Tmax.

Common Mistake

Saying maximum torque occurs at synchronous speed; torque is zero at s=0.

Quick Revision

Effect of Rotor Resistance on Maximum Torque is linked with Torque-Slip Characteristics, Induction Motors and Electrical Machines. Rotor resistance shifts the torque-slip curve horizontally, not vertically at Tmax.