Question

The charge flowing in a conductor varies with time as $Q=at-b{{t}^{2}},$ then the current changes at the rate of $(-2b)$ falls to zero after $T=\left( \frac{a}{2b} \right)$ (3) reaches a maximum and then decreases (4) will remain constant

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (B)

1 and 2 are correct

Answer 2

$Q=at-b{{t}^{2}}$ Current, $I=\frac{dQ}{dt}$
$=\frac{d}{dt}(at-b{{t}^{2}})$
$=a-2bt$ If $I=0$ then $0=a-2bt$ or $t=\frac{a}{2b}$ Also, $\frac{dI}{dt}=\frac{d}{dt}(a-2bt)$
$=-2b$
Therefore, current change at the ratio of $(-2b)$ .