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Which one of the following characteristic equations of result in the stable operation of the feedback system ?
- a)s3 +4s2 + s – 6 = 0
- b)s3 + s2 + 5s + 6 = 0
- c)s3 + 4s2 + 10s+11= 0
- d)s4 + s3 + 2s2 + 4s + 6 = 0
Correct answer is option 'C'. Can you explain this answer?
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Which one of the following characteristic equations of result in the s...
Characteristic Equation:
The characteristic equation of a feedback system is obtained by equating the denominator of the transfer function to zero. It represents the equation whose roots determine the stability of the system.
Stability in Feedback Systems:
A feedback system is said to be stable if all the poles of its characteristic equation have negative real parts. In other words, for stability, all the roots of the characteristic equation must be located in the left half of the complex plane.
Analysis of Given Options:
Let's analyze each option to determine which one results in stable operation of the feedback system.
a) s^3 + 4s^2 + s + 6 = 0:
This option does not guarantee stability since it does not satisfy the condition of having all roots with negative real parts.
b) s^3 + s^2 + 5s + 6 = 0:
This option does not guarantee stability either as it also fails to satisfy the condition of having all roots with negative real parts.
c) s^3 + 4s^2 + 10s + 11 = 0:
This option satisfies the condition of having all roots with negative real parts. Therefore, it results in the stable operation of the feedback system.
d) s^4 + s^3 + 2s^2 + 4s + 6 = 0:
This option is not considered because it is a quartic equation and not a cubic equation as required in the question.
Conclusion:
Among the given options, only option 'c' satisfies the condition of having all roots with negative real parts, resulting in the stable operation of the feedback system.
The characteristic equation of a feedback system is obtained by equating the denominator of the transfer function to zero. It represents the equation whose roots determine the stability of the system.
Stability in Feedback Systems:
A feedback system is said to be stable if all the poles of its characteristic equation have negative real parts. In other words, for stability, all the roots of the characteristic equation must be located in the left half of the complex plane.
Analysis of Given Options:
Let's analyze each option to determine which one results in stable operation of the feedback system.
a) s^3 + 4s^2 + s + 6 = 0:
This option does not guarantee stability since it does not satisfy the condition of having all roots with negative real parts.
b) s^3 + s^2 + 5s + 6 = 0:
This option does not guarantee stability either as it also fails to satisfy the condition of having all roots with negative real parts.
c) s^3 + 4s^2 + 10s + 11 = 0:
This option satisfies the condition of having all roots with negative real parts. Therefore, it results in the stable operation of the feedback system.
d) s^4 + s^3 + 2s^2 + 4s + 6 = 0:
This option is not considered because it is a quartic equation and not a cubic equation as required in the question.
Conclusion:
Among the given options, only option 'c' satisfies the condition of having all roots with negative real parts, resulting in the stable operation of the feedback system.
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Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?
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Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. 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 Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. 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 Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?.
Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. 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 Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. 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 Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?.
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Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Which one of the following characteristic equations of result in the stable operation of the feedback system ?a)s3 +4s2 + s – 6 = 0b)s3 + s2 + 5s + 6 = 0c)s3 + 4s2 + 10s+11= 0d)s4 + s3 + 2s2 + 4s + 6 = 0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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