The charge flowing in a conductor changes with time as Q(t) = α t - β t² + γ t³. Where α, β and γ are constants. Minimum value of current is: (a) β - α²3γ (b) α - 3β²γ (c) α - β²3γ (d) α - γ²3β

Answer: (c). I = dQ/dt = α - 2β t + 3γ t² For minimum, dI/dt = -2β + 6γ t = 0 ⇒ t = (β)/(3γ) Imin = α - 2β²3γ + β²3γ = α - β²3γ So the answer is (c).

The charge flowing in a conductor changes with time as Q(t) = α t - β… | JEE Main 2023 (30 Jan, Shift 1)

Q12JEE Main 2023 · 30 JAN · SHIFT 1Medium

Electric Current, Drift Velocity & Current Density

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:

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Answer: (c)

$I = \dfrac{dQ}{dt} = \alpha - 2\beta t + 3\gamma t^{2}$
For minimum, $\dfrac{dI}{dt} = -2\beta + 6\gamma t = 0 \Rightarrow t = \dfrac{\beta}{3\gamma}$
$I_{min} = \alpha - \dfrac{2\beta^{2}}{3\gamma} + \dfrac{\beta^{2}}{3\gamma} = \alpha - \dfrac{\beta^{2}}{3\gamma}$
So the answer is (c).

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