The charge flowing in a conductor charge with time as $Q (t)= αt - {βt}^{2} + {γt}^{3} .$ Where α,ß and $λ$ are constants. Minimum value of current is:

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$β - \frac{α^{2}}{3 γ}$

$α - \frac{β^{2}}{3 γ}$

$α - \frac{γ^{2}}{3 β}$

$α - \frac{3 β^{2}}{γ}$

answer is B.

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Detailed Solution

$\begin{array}{l} Q (t) = αt - {βt}^{2} + {γt}^{3} \\ I = α - 2 βt + 3 {γt}^{2} \\ For I \to min So I_{\min} = α - \frac{β^{2}}{3 γ} \\ \frac{dI}{dt} = 0 \Rightarrow t = \frac{β}{3 γ} \end{array}$

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