All identical capacitor plates each of area $A$ are arranged such that adjacent plates are at $d$ distance apart and are initially uncharged. Plates are connected to a source of emf $V$ volts as shown in figure. (dielectric constant in each shaded region is k = 2)
 

Apply Kirchhoff's Law on the equivalent circuit shown in the diagram.

Capacitance of capacitors with dielectric between the plates is $\frac{2A{\in }_0}{d}$

Capacitance of capacitors without dielectric between the plates is $\frac{A{\in }_0}{d}$

Equivalent capacitance between AB is  $\frac{26{\in }_{0}A}{3d}$

Charge on plate 3 is = $\frac{2}{3}\frac{{\epsilon }_{0}AV}{d}+\frac{{\epsilon }_{0}AV}{d}=\frac{5}{3}\frac{{\epsilon }_{0}AV}{d}$

Potential difference between the plates 4 and 7 is = $V-\frac{V}{3}=\frac{2V}{3}$

The heat produced by the system is 

$=\frac{1}{2}{C}_{eq}{V}^2=\frac{13}{3}\frac{{\epsilon }_{0}A{V}^2}{d}$