Question

The change $q$ flowing in a conductor of uniform cross section, varies with time as $q=\alpha t-\beta t^2$. Then the current

• A. decreases linearly with time
• B. reaches a maximum and then decreases
• C. falls to zero after a time $t=\alpha /2\beta$
• D. changes at the rate $-2\beta$

Answer 1

Answer: (D)

changes at the rate $-2\beta$

$q=\alpha t-\beta t^2$

$i=\frac{dq}{dt}=\alpha -2\beta t$

If $i=0$, then $\alpha -2\beta t=0⟹t=\frac{\alpha }{2\beta }$

$\frac{di}{dt}=-2\beta$