In the circuit shown, initially the switch is in position 1 for a long time. Then the switch is shifted to position 2 for a long time. Find the total heat produced in R$_2$.

After long time in positin1 the current inthe circuit is E/R$_1$

So in position 2 alsote current frm inductor would be E / R$_1$

Hence the heat produced in R$_2$ would be $ER_2 ^2/R_1$

But the answer given as $LE^2 /2R_1 ^2$

The initial *power* generated in $R_2$ is $I_0^2 R_2$ Watts - *not* $I_0 R_2^2$. But you are asked for the total *heat energy* dissipated in $R_2$ in Joules.