Consider the following statements regarding Root Locus Plot:1.Root locus starts at open-loop poles and ends at zeros.2.Number of branches equals number of poles.3.Root locus always lies in left half plane.4.Breakaway points occur on real axis.Which of the above statements is/are correct?

Correct Answer: A - 1, 2 and 4 only

Quick Concept Explanation

Branches start at open-loop poles and end at finite zeros or zeros at infinity; the number of branches equals the number of open-loop poles. Real-axis breakaway/break-in points can occur where multiple branches meet, and loci can enter the right-half plane. Key relation: Characteristic equation 1+KG(s)H(s)=0.

Exam focus: Start at poles, finish at zeros/infinity. Common trap: Root locus is not confined to the left-half plane.

Statement-wise Verification

• Statement 1 - Correct.
  Root locus starts at open-loop poles and ends at zeros.
  Branches start at open-loop poles and end at finite zeros or zeros at infinity
• Statement 2 - Correct.
  Number of branches equals number of poles.
  Branches start at open-loop poles and end at finite zeros or zeros at infinity; the number of branches equals the number of open-loop poles.
• Statement 3 - Incorrect.
  Root locus always lies in left half plane.
  Root-locus branches can cross into the right-half plane as gain varies
• Statement 4 - Correct.
  Breakaway points occur on real axis.
  Real-axis breakaway/break-in points can occur where multiple branches meet, and loci can enter the right-half plane.

Core Concept

Root locus shows closed-loop pole locations as a gain parameter varies. Branches start at open-loop poles and end at finite zeros or zeros at infinity; the number of branches equals the number of open-loop poles. Real-axis breakaway/break-in points can occur where multiple branches meet, and loci can enter the right-half plane.

Formula / Key Relationship

Characteristic equation 1+KG(s)H(s)=0.

Why the Other Options Are Wrong

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

Exam Shortcut / Approach

Start at poles, finish at zeros/infinity.

Common Mistake

Root locus is not confined to the left-half plane.

Quick Revision

Branches Poles Zeros and Breakaway Points is linked with Root Locus Rules, Root Locus and Control Systems. Start at poles, finish at zeros/infinity.