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Assertion (A): With the increase in bandwidth of the system the response of the system becomes fast.
Reason (R): Damping ratio of the system decreases with the increase in bandwidth.
Reason (R): Damping ratio of the system decreases with the increase in bandwidth.
- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Assertion (A): With the increase in bandwidth of the system the respon...
When BW is increased, the system response becomes fast due to fait in rise time (tr).
With the increase in bandwidth of the system, damping ratio (ξ) decreases.
Thus, both assertion and reason are true but, reason is not the correct explanation of assertion.
With the increase in bandwidth of the system, damping ratio (ξ) decreases.
Thus, both assertion and reason are true but, reason is not the correct explanation of assertion.
Most Upvoted Answer
Assertion (A): With the increase in bandwidth of the system the respon...
Explanation:
The statement "With the increase in bandwidth of the system the response of the system becomes fast" is true because bandwidth is a measure of the frequency range that a system can handle. A system with a higher bandwidth can handle higher frequency signals, and thus respond faster to changes in the input signal.
However, the statement "Damping ratio of the system decreases with the increase in bandwidth" is not always true. The damping ratio is a measure of how quickly the system oscillations decay in response to an input. It is related to the natural frequency of the system and the amount of damping in the system.
Counterexample:
Consider a system with a low damping ratio and a high natural frequency. This system will have a high bandwidth because it can respond to high-frequency signals. However, the damping ratio is low, meaning that the system will oscillate for a long time before settling to a steady-state response. Therefore, in this case, the response of the system is not necessarily fast even though the bandwidth is high.
Conclusion:
Therefore, both statements are true, but the second statement does not always provide a correct explanation for the first statement. The relationship between bandwidth and response time is more complex and depends on other factors such as the damping ratio and natural frequency of the system.
The statement "With the increase in bandwidth of the system the response of the system becomes fast" is true because bandwidth is a measure of the frequency range that a system can handle. A system with a higher bandwidth can handle higher frequency signals, and thus respond faster to changes in the input signal.
However, the statement "Damping ratio of the system decreases with the increase in bandwidth" is not always true. The damping ratio is a measure of how quickly the system oscillations decay in response to an input. It is related to the natural frequency of the system and the amount of damping in the system.
Counterexample:
Consider a system with a low damping ratio and a high natural frequency. This system will have a high bandwidth because it can respond to high-frequency signals. However, the damping ratio is low, meaning that the system will oscillate for a long time before settling to a steady-state response. Therefore, in this case, the response of the system is not necessarily fast even though the bandwidth is high.
Conclusion:
Therefore, both statements are true, but the second statement does not always provide a correct explanation for the first statement. The relationship between bandwidth and response time is more complex and depends on other factors such as the damping ratio and natural frequency of the system.
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Assertion (A): With the increase in bandwidth of the system the response of the system becomes fast.Reason (R): Damping ratio of the system decreases with the increase in bandwidth.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer?
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ample number of questions to practice Assertion (A): With the increase in bandwidth of the system the response of the system becomes fast.Reason (R): Damping ratio of the system decreases with the increase in bandwidth.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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