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)

$ 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) $ .