Question

The charge flowing through a resistance $R$ varies with time as $Q=2t-8t^2$. The total heat produced (in joules) in the resistance is
$(\text{for}0\le t\le \frac{1}{8}\text{s})$

• A. $\frac{R}{6}$
• B. $\frac{R}{3}$
• C. $\frac{R}{2}$
• D. $R$

Answer 1

The correct option is A $\frac{R}{6}$

Given, $Q=2t-8t^2$
We know that, $i=\frac{dQ}{dt}=2-16t$
Heat produced $=R{\int }_0^{1/8}{\left(i\right)}^2.dt$
$=R{\int }_0^{1/8}{(2-16t)}^2.dt$
$=R{\left[\frac{(2-16t{)}^3}{3(-16)}\right]}_0^{1/8}$
$=-\frac{R}{48}[0-8]$
$=\frac{R}{6}\text{joules}$