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The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:
- a)0° and 270°
- b)0° and 180°
- c)90° and 270°
- d)90° and 180°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)...
Answer: c
Explanation: P-Z =2
Angle of asymptote = (2q+1)180°/P-Z
Angle are 90° and 270°.
Explanation: P-Z =2
Angle of asymptote = (2q+1)180°/P-Z
Angle are 90° and 270°.
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Community Answer
The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)...
We can find the angles of asymptotes using the following formula:
θa = (2n + 1)180°/N
where θa is the angle of the asymptote, n is the index of the asymptote (starting from 0), and N is the number of branches of the root locus.
First, we need to find the number of branches of the root locus. We can do this by applying the Routh-Hurwitz criterion to the characteristic equation:
s^3 + 5s^2 + (K-2)s + K = 0
The Routh-Hurwitz table is:
1 | 1 K-2
--|--------
5 | 5+K 0
- | K 0
For the root locus to exist, the number of sign changes in the first column of the Routh-Hurwitz table must be equal to the number of roots in the right half of the s-plane. In this case, there are no sign changes, so all three roots are in the left half of the s-plane. Therefore, there are three branches of the root locus.
Now we can find the angles of the asymptotes:
θa = (2n + 1)180°/N
For n = 0:
θa1 = (2(0) + 1)180°/3 = 60°
For n = 1:
θa2 = (2(1) + 1)180°/3 = 180°
For n = 2:
θa3 = (2(2) + 1)180°/3 = 300°
Therefore, the angles of the asymptotes are 60°, 180°, and 300°.
θa = (2n + 1)180°/N
where θa is the angle of the asymptote, n is the index of the asymptote (starting from 0), and N is the number of branches of the root locus.
First, we need to find the number of branches of the root locus. We can do this by applying the Routh-Hurwitz criterion to the characteristic equation:
s^3 + 5s^2 + (K-2)s + K = 0
The Routh-Hurwitz table is:
1 | 1 K-2
--|--------
5 | 5+K 0
- | K 0
For the root locus to exist, the number of sign changes in the first column of the Routh-Hurwitz table must be equal to the number of roots in the right half of the s-plane. In this case, there are no sign changes, so all three roots are in the left half of the s-plane. Therefore, there are three branches of the root locus.
Now we can find the angles of the asymptotes:
θa = (2n + 1)180°/N
For n = 0:
θa1 = (2(0) + 1)180°/3 = 60°
For n = 1:
θa2 = (2(1) + 1)180°/3 = 180°
For n = 2:
θa3 = (2(2) + 1)180°/3 = 300°
Therefore, the angles of the asymptotes are 60°, 180°, and 300°.
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The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer?.
The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of asymptotes of the root loci of the equation s3+5s2+(K+2)s+K=0 are:a)0° and 270°b)0° and 180°c)90° and 270°d)90° and 180°Correct answer is option 'C'. Can you explain this answer?.
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