An induction motor operates at a slip of 5% with a supply frequency of 50 Hz.1.Rotor frequency is approximately2.5 Hz.2.Rotor current frequency becomes zero at synchronous speed.3.Rotor frequency equals supply frequency at standstill.4.Rotor frequency is independent of slip.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 3 only

Quick Concept Explanation

Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f. Key relation: s=(N_s−N)/N_s; f_r=s f_s.

Exam focus: Standstill: s=1; synchronous speed: s=0. Common trap: Rotor frequency is not independent of slip.

Statement-wise Verification

• Statement 1 - Correct.
  Rotor frequency is approximately 2.5 Hz.
  Rotor frequency fr=s f=0.05×50=2.5 Hz.
• Statement 2 - Correct.
  Rotor current frequency becomes zero at synchronous speed.
  Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.
• Statement 3 - Correct.
  Rotor frequency equals supply frequency at standstill.
  Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.
• Statement 4 - Incorrect.
  Rotor frequency is independent of slip.
  The correct principle is: Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.

Core Concept

Slip measures the difference between synchronous speed and rotor speed. Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. These relations are fundamental to induction-motor torque and rotor-circuit behavior.

Formula / Key Relationship

s=(N_s−N)/N_s; f_r=s f_s.

Step-by-Step Check

Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f.

Why the Other Options Are Wrong

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

Exam Shortcut / Approach

Standstill: s=1; synchronous speed: s=0.

Common Mistake

Rotor frequency is not independent of slip.

Quick Revision

Rotor Frequency versus Slip is linked with Slip and Rotor Frequency, Induction Motors and Electrical Machines. Standstill: s=1; synchronous speed: s=0.