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Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true but R is not the 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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Assertion (A): The Shannon-Hartley law shows that we can exchange incr...
According to Shannon-Hartley faw, the channel capacity is expressed as
Thus, if signal power is more, bandwidth will be less and vice-versa. Thus, assertion is a true statement. Reason is also a true statement because the rate of information that can be transmitted depends on bandwidth and signal to noise power. Thus, both assertion and reason are true but reason is not the correct explanation of assertion.
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Assertion (A): The Shannon-Hartley law shows that we can exchange incr...
The Shannon-Hartley law is a fundamental concept in information theory that relates the capacity of a communication channel to the bandwidth and signal power of the system. Let's analyze the given assertion and reason in detail:
Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
Explanation:
To understand the assertion and reason, it is necessary to have a basic understanding of the Shannon-Hartley law.
The Shannon-Hartley law, also known as the Shannon capacity formula or the Hartley-Shannon theorem, provides a theoretical limit on the maximum data rate that can be transmitted reliably over a communication channel. It states that the capacity C of a channel in bits per second (bps) is given by the formula:
C = B log2(1 + S/N)
Where B is the bandwidth of the channel in hertz (Hz), S is the signal power in watts (W), and N is the noise power in watts (W).
Now, let's analyze the assertion and reason separately:
Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
This assertion is true. According to the Shannon-Hartley law, the capacity of a channel is directly proportional to the bandwidth and logarithmically proportional to the signal power. This means that if we increase the bandwidth, we can decrease the signal power while maintaining the same capacity. Similarly, if we decrease the bandwidth, we can increase the signal power to compensate and still achieve the same capacity.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
This reason is also true. The bandwidth and signal power of a system play a crucial role in determining the rate of information transmission. The bandwidth determines the range of frequencies that can be used for transmission, while the signal power represents the strength of the signal. Both factors place restrictions on the rate of information that can be transmitted by a channel. The Shannon-Hartley law quantifies this relationship by providing a formula that relates the capacity of the channel to the bandwidth and signal power.
Therefore, both the assertion and reason are true. However, the reason does not provide a correct explanation for the assertion. The Shannon-Hartley law itself explains the relationship between bandwidth, signal power, and channel capacity, while the reason simply states that the bandwidth and signal power place a restriction on the rate of information transmission without explaining how they are related.
Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
Explanation:
To understand the assertion and reason, it is necessary to have a basic understanding of the Shannon-Hartley law.
The Shannon-Hartley law, also known as the Shannon capacity formula or the Hartley-Shannon theorem, provides a theoretical limit on the maximum data rate that can be transmitted reliably over a communication channel. It states that the capacity C of a channel in bits per second (bps) is given by the formula:
C = B log2(1 + S/N)
Where B is the bandwidth of the channel in hertz (Hz), S is the signal power in watts (W), and N is the noise power in watts (W).
Now, let's analyze the assertion and reason separately:
Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
This assertion is true. According to the Shannon-Hartley law, the capacity of a channel is directly proportional to the bandwidth and logarithmically proportional to the signal power. This means that if we increase the bandwidth, we can decrease the signal power while maintaining the same capacity. Similarly, if we decrease the bandwidth, we can increase the signal power to compensate and still achieve the same capacity.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.
This reason is also true. The bandwidth and signal power of a system play a crucial role in determining the rate of information transmission. The bandwidth determines the range of frequencies that can be used for transmission, while the signal power represents the strength of the signal. Both factors place restrictions on the rate of information that can be transmitted by a channel. The Shannon-Hartley law quantifies this relationship by providing a formula that relates the capacity of the channel to the bandwidth and signal power.
Therefore, both the assertion and reason are true. However, the reason does not provide a correct explanation for the assertion. The Shannon-Hartley law itself explains the relationship between bandwidth, signal power, and channel capacity, while the reason simply states that the bandwidth and signal power place a restriction on the rate of information transmission without explaining how they are related.
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Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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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Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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?.
Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the 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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