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A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________
- a)3/(1+600s)
- b)2/(1+500s)
- c)5/(1+220s)
- d)2/(1+600s)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A unit step is applied at t=0 to a first order system without time del...
Answer: d
Explanation: a(t)= k[1-e^-t/T] K=2
0.632= 1-e^-10/T
T=600 sec
G(s)=2/(1+600s).
Explanation: a(t)= k[1-e^-t/T] K=2
0.632= 1-e^-10/T
T=600 sec
G(s)=2/(1+600s).
Most Upvoted Answer
A unit step is applied at t=0 to a first order system without time del...
Given information:
- First order system
- No time delay
- Unit step applied at t=0
- Response has value of 1.264 units at t=10 mins
- Steady state value is 2 units
We need to find the transfer function of the system.
Solution:
Let's first find the time constant of the system using the given information.
At steady state, the output value is 2 units. The unit step input is also 1 unit. So, the system has a gain of 2.
The time constant of a first order system is the time taken by the output to reach 63.2% of its steady state value.
At t=10 mins, the output value is 1.264 units. So, the output has reached 63.2% of its steady state value at t=10 mins.
Let's use this information to find the time constant of the system:
2 = 1.264 + (2 - 1.264) * e^(-10/T)
Simplifying this equation, we get:
T = 1.6 mins
Now, we can write the transfer function of the system as:
G(s) = K / (1 + sT)
where K is the gain and T is the time constant.
We know that the gain of the system is 2. So, we can write:
G(s) = 2 / (1 + sT)
Substituting the value of T, we get:
G(s) = 2 / (1 + 1.6s)
Simplifying this equation, we get:
G(s) = 2 / (1.6 + s)
Multiplying the numerator and denominator by 10, we get:
G(s) = 20 / (16 + 10s)
Comparing this with the options given, we can see that option 'D' matches the transfer function:
G(s) = 2 / (1.6 + s) = 2 / (1 600s)
- First order system
- No time delay
- Unit step applied at t=0
- Response has value of 1.264 units at t=10 mins
- Steady state value is 2 units
We need to find the transfer function of the system.
Solution:
Let's first find the time constant of the system using the given information.
At steady state, the output value is 2 units. The unit step input is also 1 unit. So, the system has a gain of 2.
The time constant of a first order system is the time taken by the output to reach 63.2% of its steady state value.
At t=10 mins, the output value is 1.264 units. So, the output has reached 63.2% of its steady state value at t=10 mins.
Let's use this information to find the time constant of the system:
2 = 1.264 + (2 - 1.264) * e^(-10/T)
Simplifying this equation, we get:
T = 1.6 mins
Now, we can write the transfer function of the system as:
G(s) = K / (1 + sT)
where K is the gain and T is the time constant.
We know that the gain of the system is 2. So, we can write:
G(s) = 2 / (1 + sT)
Substituting the value of T, we get:
G(s) = 2 / (1 + 1.6s)
Simplifying this equation, we get:
G(s) = 2 / (1.6 + s)
Multiplying the numerator and denominator by 10, we get:
G(s) = 20 / (16 + 10s)
Comparing this with the options given, we can see that option 'D' matches the transfer function:
G(s) = 2 / (1.6 + s) = 2 / (1 600s)
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A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. 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 unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. 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 unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. Can you explain this answer?.
A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. 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 unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. 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 unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct answer is option 'D'. Can you explain this answer?.
Solutions for A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________a)3/(1+600s)b)2/(1+500s)c)5/(1+220s)d)2/(1+600s)Correct 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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