Question

$A$ time varying current $i$ is passed through a resistance $R$ as shown in figure. The total heat generated in the resistance is

• A. $13(i_0{)}^{2}T{t}_0$
• B. $11(i_0{)}^{2}T{t}_0$
• C. $15(i_0{)}^{2}T{t}_0$
• D. $17(i_0{)}^{2}T{t}_0$

Answer 1

The correct option is A $13(i_0{)}^{2}T{t}_0$

From $t=0\to t_0$
From the graph
$i=\frac{3i_0}{i_0}t$ (from straight line equation)

We know that, $H=i^{2}R{t}^2$
Total heat produced
$={\int }_0^{t_0}(\frac{3i_0}{t_0}{)}^2$ $Rdt+\left(3i_0{)}^{2}R\right(2t_0-t_0)+(i_0{)}^{2}R(3t_0-2t_0)$
$=3(i_0{)}^{2}R{t}_0+9(i_0{)}^{2}R{t}_0+(i_0{)}^2$$R{t}_0=13(i_0{)}^{2}R{t}_0$
Hence, option $\left(b\right)$ is correct.