Initially, switch S is connected to position 1 for a long time as shown in figure. The net amount of heat generated in the circuit after it is shifted to position 2 is:-
 

$U_i=\frac{1}{2}C{\epsilon }_1^2$

$U_f=\frac{1}{2}C{\epsilon }_2^2,\Delta U=\frac{1}{2}C({\epsilon }_2^2-{\epsilon }_1^2)$

$Q_{in}=+C{\epsilon }_1,Q_f=-C{\epsilon }_2,\Delta Q=|Q_f-Q_i|$

$=C({\epsilon }_2+{\epsilon }_1)$

 Work done by battery

$W_b={\epsilon }_2\Delta Q=C({\epsilon }_2+{\epsilon }_1){\epsilon }_2$

Heat generated  $=W_b-\Delta U$

$=C{\epsilon }_2^2+C{\epsilon }_1{\epsilon }_2-\frac{1}{2}C({\epsilon }_2^2-{\epsilon }_1^2)$

$=\frac{1}{2}C({\epsilon }_2^2+{\epsilon }_1^2+2{\epsilon }_1{\epsilon }_2)=\frac{1}{2}C{({\epsilon }_1+{\epsilon }_2)}^2$