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In time domain specification, the time delay is the time required for the response to reach
- a)25% of final value
- b)50% of the final value
- c)10% of the final value
- d)63.3% of the final value
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In time domain specification, the time delay is the time required for ...
Delay time (td) is the time required for the response curve to reach 50% of the final value.
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In time domain specification, the time delay is the time required for ...
Time Domain Specification and Time Delay
Time domain specification is a measure of the response characteristics of a system in the time domain. It provides information about how the system behaves over time, including the time required for the response to reach certain values.
Definition of Time Delay
The time delay is the time required for the response of a system to reach a certain percentage of its final value. It is often used to evaluate the speed or time response of a system.
Options for Time Delay
The given options for the time delay are:
a) 25% of final value
b) 50% of final value
c) 10% of final value
d) 63.3% of final value
Explanation of Correct Answer
The correct answer is option 'B', which states that the time delay is the time required for the response to reach 50% of the final value.
This is based on the concept of the standard settling time, which is defined as the time required for the response to stay within a certain percentage of the final value. In many systems, the settling time is considered to be the time it takes for the response to reach 98% of the final value.
In the case of a first-order system, the response reaches its final value exponentially. The time constant (τ) of the system determines the rate at which the response reaches the final value. It is defined as the time required for the response to reach approximately 63.2% of the final value.
Since the question is asking for the time delay to reach a certain percentage, the correct answer can be determined by finding the time at which the response reaches that percentage.
For a first-order system, the time required to reach 50% of the final value is approximately equal to 0.69 times the time constant (τ). This is derived from the formula for the exponential response of a first-order system.
Therefore, the correct answer is option 'B', as it represents the time delay required for the response to reach 50% of the final value.
Time domain specification is a measure of the response characteristics of a system in the time domain. It provides information about how the system behaves over time, including the time required for the response to reach certain values.
Definition of Time Delay
The time delay is the time required for the response of a system to reach a certain percentage of its final value. It is often used to evaluate the speed or time response of a system.
Options for Time Delay
The given options for the time delay are:
a) 25% of final value
b) 50% of final value
c) 10% of final value
d) 63.3% of final value
Explanation of Correct Answer
The correct answer is option 'B', which states that the time delay is the time required for the response to reach 50% of the final value.
This is based on the concept of the standard settling time, which is defined as the time required for the response to stay within a certain percentage of the final value. In many systems, the settling time is considered to be the time it takes for the response to reach 98% of the final value.
In the case of a first-order system, the response reaches its final value exponentially. The time constant (τ) of the system determines the rate at which the response reaches the final value. It is defined as the time required for the response to reach approximately 63.2% of the final value.
Since the question is asking for the time delay to reach a certain percentage, the correct answer can be determined by finding the time at which the response reaches that percentage.
For a first-order system, the time required to reach 50% of the final value is approximately equal to 0.69 times the time constant (τ). This is derived from the formula for the exponential response of a first-order system.
Therefore, the correct answer is option 'B', as it represents the time delay required for the response to reach 50% of the final value.
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