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Branches Tending to Infinity

The loop transfer function G(s)H(s) of a unity feedback system is given by G(s) H(s) = (s + 2) / ((s + 4) (s + 5) (s + 6)). How many branches of root locus will tend towards infinity?

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Answer & Explanation

Correct AnswerC. 2

Quick Explanation

A root locus has one branch for each open-loop pole. The number of branches that terminate at infinity equals the number of poles minus the number of finite zeros. Here there are 3 poles and 1 zero, so 2 branches go to infinity.

Formula / Key Relation

Number of asymptotes = P−Z = 3−1 = 2

Branches Tending to Infinity explanatory diagram

Detailed Explanation

Correct Answer

C — 2

Concept and Reasoning

Calculation / Key Relation

P=3

Z=1

Branches to infinity=P−Z=2

Exam Takeaway

Count poles and finite zeros before drawing the locus.

Common Mistake

Do not count the finite zero as an asymptote endpoint at infinity.

Quick Trick

Count poles and finite zeros before drawing the locus.

Common Mistake

Do not count the finite zero as an asymptote endpoint at infinity.

Exam Tip

Count poles and finite zeros before drawing the locus.

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QP-112-202425.pdf2024Q. 17

Branches Tending to Infinity

Quick Explanation

Formula / Key Relation

Detailed Explanation

Correct Answer

Concept and Reasoning

Calculation / Key Relation

Exam Takeaway

Common Mistake

Quick Trick

Common Mistake

Exam Tip

Previous Exam Appearances

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