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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________
- a)a = 5 and k = 12
- b)a = 10 and k = 5
- c)a = 5 and k = 10
- d)a = 8 and k = 9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A first order system and its response to a unit step input are shown i...
The given figure represents a first-order system and its response to a unit step input. We need to determine the values of the system parameters.
To analyze the system's response, we can observe the following key points from the figure:
1. Steady-state value (Final Value): The steady-state value of the system response is the value it approaches after a long time. In this case, the steady-state value is approximately 10.
2. Time constant (τ): The time constant of a first-order system is the time it takes for the system to reach approximately 63.2% of its steady-state value. In this case, it can be observed that the system reaches 63.2% of its steady-state value at approximately t = 5 seconds.
Based on these observations, we can determine the values of the system parameters as follows:
1. Steady-state value (Final Value):
- From the figure, it can be observed that the steady-state value is approximately 10.
- Therefore, the value of parameter k is 10.
2. Time constant (τ):
- From the figure, it can be observed that the system reaches 63.2% of its steady-state value at approximately t = 5 seconds.
- The time constant of a first-order system is equal to the time it takes to reach 63.2% of its steady-state value.
- Therefore, the value of parameter a is 5.
Hence, the correct answer is option 'C' - a = 5 and k = 10.
This means that the transfer function of the given first-order system can be represented as:
G(s) = k / (s + a)
= 10 / (s + 5)
This transfer function describes the mathematical relationship between the input and output of the system.
To analyze the system's response, we can observe the following key points from the figure:
1. Steady-state value (Final Value): The steady-state value of the system response is the value it approaches after a long time. In this case, the steady-state value is approximately 10.
2. Time constant (τ): The time constant of a first-order system is the time it takes for the system to reach approximately 63.2% of its steady-state value. In this case, it can be observed that the system reaches 63.2% of its steady-state value at approximately t = 5 seconds.
Based on these observations, we can determine the values of the system parameters as follows:
1. Steady-state value (Final Value):
- From the figure, it can be observed that the steady-state value is approximately 10.
- Therefore, the value of parameter k is 10.
2. Time constant (τ):
- From the figure, it can be observed that the system reaches 63.2% of its steady-state value at approximately t = 5 seconds.
- The time constant of a first-order system is equal to the time it takes to reach 63.2% of its steady-state value.
- Therefore, the value of parameter a is 5.
Hence, the correct answer is option 'C' - a = 5 and k = 10.
This means that the transfer function of the given first-order system can be represented as:
G(s) = k / (s + a)
= 10 / (s + 5)
This transfer function describes the mathematical relationship between the input and output of the system.
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Community Answer
A first order system and its response to a unit step input are shown i...
time constant = 0.2 sec.
1/a = 0.2
a = 5
final value =
K/a = 2
K = 10.
1/a = 0.2
a = 5
final value =
K/a = 2
K = 10.
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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer?.
A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer?.
Solutions for A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A first order system and its response to a unit step input are shown in figure below. The system parameters are____________a)a = 5 and k = 12b)a = 10 and k = 5c)a = 5 and k = 10d)a = 8 and k = 9Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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