Question

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 : [Jan. 30, 2023 (I)] (a) \( \alpha=\frac{3 \beta^{2}}{\gamma} \) (b) \( \alpha-\frac{\gamma^{2}}{3 \beta} \) (c) \( \beta-\frac{\alpha^{2}}{3 \gamma} \) (d) \( \alpha-\frac{\beta^{2}}{3 \gamma} \)

Answer 1

Correct option is (d) \(\alpha - \frac {\beta ^ 2}{3\gamma}\)

Given here,

\(Q - \alpha t - \beta t ^ 2 + \gamma t ^ 3\)

Current flowing through conductor is given by