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A thermometer requires 1 minute to indicate 98% of its final response to a step input. If it is a first order system the time constant is
- a)1 minute
- b)0.5 minute
- c)0.25 minute
- d)0.1 minute
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A thermometer requires 1 minute to indicate 98% of its final response ...
0.98 = 1 - e-1/T or T = 0.25 minute.
Most Upvoted Answer
A thermometer requires 1 minute to indicate 98% of its final response ...
Given Information:
- A thermometer requires 1 minute to indicate 98% of its final response to a step input.
- First Order System
To find: Time Constant (τ)
Explanation:
A First Order System can be represented by the following transfer function:
G(s) = K / (τs + 1)
Where,
K = Steady State Gain
τ = Time Constant
In this case, the system is a First Order System, and it takes 1 minute to indicate 98% of its final response to a step input.
We know that for a First Order System, the time constant (τ) is the time taken for the system response to reach 63.2% of its final value.
So, we can use the given information to find the time constant (τ) as follows:
- At t = 0, the system response is 0%.
- At t = 1 minute, the system response is 98%.
- So, at t = τ, the system response is 63.2% (approx).
From the above observations, we can write the following equation:
0.632 = 1 - e^(-1/τ)
Solving for τ, we get:
τ = 0.25 minutes
Therefore, the time constant (τ) of the given First Order System is 0.25 minutes.
Answer: Option (c) 0.25 minute.
- A thermometer requires 1 minute to indicate 98% of its final response to a step input.
- First Order System
To find: Time Constant (τ)
Explanation:
A First Order System can be represented by the following transfer function:
G(s) = K / (τs + 1)
Where,
K = Steady State Gain
τ = Time Constant
In this case, the system is a First Order System, and it takes 1 minute to indicate 98% of its final response to a step input.
We know that for a First Order System, the time constant (τ) is the time taken for the system response to reach 63.2% of its final value.
So, we can use the given information to find the time constant (τ) as follows:
- At t = 0, the system response is 0%.
- At t = 1 minute, the system response is 98%.
- So, at t = τ, the system response is 63.2% (approx).
From the above observations, we can write the following equation:
0.632 = 1 - e^(-1/τ)
Solving for τ, we get:
τ = 0.25 minutes
Therefore, the time constant (τ) of the given First Order System is 0.25 minutes.
Answer: Option (c) 0.25 minute.
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A thermometer requires 1 minute to indicate 98% of its final response to a step input. If it is a first order system the time constant isa)1 minuteb)0.5 minutec)0.25 minuted)0.1 minuteCorrect answer is option 'C'. Can you explain this answer?
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