Question

The charge flowing through a resistance $R$ varies with time $t$ as $Q=at-b{t}^2$, where $a$ and $b$ are positive constants. Calculate the total heat produced in $R$.

Answer 1

$Q=at-b{t}^{2}i=\frac{dq}{dt}=(a-2bt)A$

Heat produced $=i^{2}Rt$

$=(a-2bt{)}^2$ Rt Joules