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The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B?
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The charge flowing in a conductor varies with time as Q=at-bt2 . Then ...
**Solution:**
The given charge flowing in a conductor is given by the equation Q = at - bt^2.
To find the current, we need to take the derivative of Q with respect to time.
**Finding the current:**
Differentiating Q with respect to time, we get:
dQ/dt = a - 2bt
So, the current I is given by:
I = dQ/dt = a - 2bt
**Analyzing the options:**
A) Decreases linearly with time:
From the expression of current I = a - 2bt, we can see that the current decreases linearly with time since the coefficient of t is negative.
B) Reaches a maximum and then decreases:
To find the maximum point of the current, we need to find the time when dI/dt = 0.
dI/dt = -2b
Setting dI/dt = 0, we get:
-2b = 0
This implies that b = 0, which contradicts the given equation. Therefore, the statement is incorrect.
C) Falls to zero after time t = a/2b:
To find the time when the current falls to zero, we need to set I = 0 and solve for t.
0 = a - 2bt
2bt = a
t = a/2b
Therefore, the statement is correct.
D) Changes at a rate -2b:
From the expression of current I = a - 2bt, we can see that the rate of change of current with time is -2b.
Therefore, the statement is correct.
**Conclusion:**
The incorrect statement is B) Reaches a maximum and then decreases.
The given charge flowing in a conductor is given by the equation Q = at - bt^2.
To find the current, we need to take the derivative of Q with respect to time.
**Finding the current:**
Differentiating Q with respect to time, we get:
dQ/dt = a - 2bt
So, the current I is given by:
I = dQ/dt = a - 2bt
**Analyzing the options:**
A) Decreases linearly with time:
From the expression of current I = a - 2bt, we can see that the current decreases linearly with time since the coefficient of t is negative.
B) Reaches a maximum and then decreases:
To find the maximum point of the current, we need to find the time when dI/dt = 0.
dI/dt = -2b
Setting dI/dt = 0, we get:
-2b = 0
This implies that b = 0, which contradicts the given equation. Therefore, the statement is incorrect.
C) Falls to zero after time t = a/2b:
To find the time when the current falls to zero, we need to set I = 0 and solve for t.
0 = a - 2bt
2bt = a
t = a/2b
Therefore, the statement is correct.
D) Changes at a rate -2b:
From the expression of current I = a - 2bt, we can see that the rate of change of current with time is -2b.
Therefore, the statement is correct.
**Conclusion:**
The incorrect statement is B) Reaches a maximum and then decreases.
Community Answer
The charge flowing in a conductor varies with time as Q=at-bt2 . Then ...
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The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B?
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The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B?.
The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The charge flowing in a conductor varies with time as Q=at-bt2 . Then for current, which statement is incorrect. A) decreases linearly with time B) reaches a maximum and then decreases C) fall to zero after time t=a/2b D) changes at a rate -2b Options: 1) A, B, D 2) A, C, D 3) B, C 4) Only B?.
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