Q 12-03-117JEE MainJEE Main 2023 (30 Jan, Shift 1)Medium
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
Answer: (D) $\alpha-\dfrac{\beta^2}{3\gamma}$
$I=\dfrac{dQ}{dt}=\alpha-2\beta t+3\gamma t^2$. $\dfrac{dI}{dt}=0\Rightarrow t=\dfrac{\beta}{3\gamma}$.
$$I_{min}=\alpha-\frac{2\beta^2}{3\gamma}+\frac{\beta^2}{3\gamma}=\alpha-\frac{\beta^2}{3\gamma}$$
Solution by Sreeraj P, M.Sc Physics