The charge flowing through a conductor varies with time as $Q = a t - b t^{2}$ . Then, the current

decreases linearly with time

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reaches a maximum and then decreases

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falls to zero at time

t = a / 2 b

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changes at a rate

- 2 b

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Solution

The correct options are
A decreases linearly with time
C falls to zero at time $t = a / 2 b$
D changes at a rate $- 2 b$
Charge $Q = a t - b t^{2}$
Current $I = \frac{d Q}{d t} = a - 2 b t$
When $I = 0 \Rightarrow a - 2 b t = 0$
$∴ t = \frac{a}{2 b}$
Current rate , $\frac{d I}{d t} = - 2 b$

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