Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
The charge flowing in a conductor varies with time as\[Q=at-b{{t}^{2}},\]then the current: (1) reaches a maximum and then decreases (2) falls to zero after \[t=a/2b\] (3) changes at the rate of\[(-2\text{ }b)\] (4) will remain constantA) 1 and 2 are correct
B) 2 and 3 are correct
C) 1 and 4 are correct
D) 1, 2 and 3 are correct
Correct Answer: B
Solution :
give \[Q=at-b{{t}^{2}}\] current, \[I=\frac{dQ}{dt}\] \[=\frac{d}{dt}(at-b{{t}^{2}})\] \[=a-2bt\] If\[I=0,\]then\[0=a-2bt\]or\[t=a/2b\] Also, \[\frac{dI}{dt}=\frac{d}{dt}(a-2bt)=-2b\] Therefore current changes at the ratio of\[(-2b)\]
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