The charge flowing in a conductor changes with time as $Q ( t )=\alpha t -\beta t ^2+\gamma t ^3$. Where $\alpha, \beta$ and $\gamma$ are constants. Minimum value of current is :
JEE MAIN 2023, Medium
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$Q=\left(\alpha t-\beta t^2+\gamma t^3\right)$
$i=\frac{d Q}{d t}=\left(\alpha-2 \beta t+3 \gamma t^2\right)$
$\frac{d i}{d t}=(3 \gamma t-2 \beta)=0$
$\Rightarrow t=\frac{\beta}{3 \gamma}$
$i=\left(\alpha-2 \beta t+3 \gamma t^2\right)=\left(\alpha-\frac{\beta^2}{3 \gamma}\right)$
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