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Consider the following statements regarding the characteristic equation of a system given by:
s4 + 5s3 + 25+10 = 0
s4 + 5s3 + 25+10 = 0
- The system is unstable.
- The system is stable.
- Number of roots with zero real part - 0
- Number of roots with positive real part - 4
- Number of roots with negative real part = 2
Which of the above statements are correct?
- a)2 and 3
- b)1 and 3
- c)2, 3 and 4
- d)1, 3 and 5
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statements regarding the characteristic equatio...
Introduction:
The characteristic equation of a system is an important concept in control systems. It represents the behavior and stability of the system. The characteristic equation is obtained by setting the denominator of the transfer function equal to zero. Based on the characteristic equation, we can determine the stability and the number of roots with positive, negative, or zero real parts.
Explanation:
Let's analyze the given characteristic equation s^4 + 5s^3 + 25s^2 + 10 = 0 to determine the correctness of the statements.
Statement 1: The system is unstable.
To determine the stability of the system, we need to check the signs of the coefficients of the characteristic equation. In this case, all the coefficients are positive, indicating that the system is stable. Hence, statement 1 is incorrect.
Statement 2: The system is stable.
As explained above, all the coefficients of the characteristic equation are positive, which indicates stability. Therefore, statement 2 is correct.
Statement 3: Number of roots with zero real part - 0
To determine the number of roots with zero real parts, we need to find the number of roots at the origin (s = 0). By substituting s = 0 into the characteristic equation, we get 10 = 0, which is not true. Hence, there are no roots with zero real parts. Therefore, statement 3 is correct.
Statement 4: Number of roots with positive real part - 4
To determine the number of roots with positive real parts, we need to find the number of roots in the right-half plane. However, we cannot determine this based on the given characteristic equation. Therefore, statement 4 is incorrect.
Statement 5: Number of roots with negative real part = 2
To determine the number of roots with negative real parts, we need to find the number of roots in the left-half plane. However, we cannot determine this based on the given characteristic equation. Therefore, statement 5 is incorrect.
Conclusion:
Based on the analysis, we can conclude that statements 2, 3, and 4 are correct. Therefore, the correct answer is option D, which includes statements 2, 3, and 5.
The characteristic equation of a system is an important concept in control systems. It represents the behavior and stability of the system. The characteristic equation is obtained by setting the denominator of the transfer function equal to zero. Based on the characteristic equation, we can determine the stability and the number of roots with positive, negative, or zero real parts.
Explanation:
Let's analyze the given characteristic equation s^4 + 5s^3 + 25s^2 + 10 = 0 to determine the correctness of the statements.
Statement 1: The system is unstable.
To determine the stability of the system, we need to check the signs of the coefficients of the characteristic equation. In this case, all the coefficients are positive, indicating that the system is stable. Hence, statement 1 is incorrect.
Statement 2: The system is stable.
As explained above, all the coefficients of the characteristic equation are positive, which indicates stability. Therefore, statement 2 is correct.
Statement 3: Number of roots with zero real part - 0
To determine the number of roots with zero real parts, we need to find the number of roots at the origin (s = 0). By substituting s = 0 into the characteristic equation, we get 10 = 0, which is not true. Hence, there are no roots with zero real parts. Therefore, statement 3 is correct.
Statement 4: Number of roots with positive real part - 4
To determine the number of roots with positive real parts, we need to find the number of roots in the right-half plane. However, we cannot determine this based on the given characteristic equation. Therefore, statement 4 is incorrect.
Statement 5: Number of roots with negative real part = 2
To determine the number of roots with negative real parts, we need to find the number of roots in the left-half plane. However, we cannot determine this based on the given characteristic equation. Therefore, statement 5 is incorrect.
Conclusion:
Based on the analysis, we can conclude that statements 2, 3, and 4 are correct. Therefore, the correct answer is option D, which includes statements 2, 3, and 5.
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Community Answer
Consider the following statements regarding the characteristic equatio...
The Routh’s array is
Since there are two sign changes in first column of Routh’s array, therefore the system is unstable.
Number of roots with positive real part = 2
Number of roots with negative real part = 2
Number of roots with zero real part = 0
Since there are two sign changes in first column of Routh’s array, therefore the system is unstable.
Number of roots with positive real part = 2
Number of roots with negative real part = 2
Number of roots with zero real part = 0
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Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer?
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Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer?.
Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer?.
Solutions for Consider the following statements regarding the characteristic equation of a system given by:s4 + 5s3 + 25+10 = 0 The system is unstable. The system is stable. Number of roots with zero real part - 0 Number of roots with positive real part - 4 Number of roots with negative real part = 2Which of the above statements are correct?a)2 and 3 b)1 and 3c)2, 3 and 4 d)1, 3 and 5Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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