Two condensers of capacities 2C and C are joined in parallel and charged upto potential V. The battery is removed and the condenser of capacity C is filled completely with a medium of dielectric constant K. What will be the new potential difference across the capacitors?

3V/(K+2)

When battery is removed , the charge Q remains constant even after insertion of the dielectric (at battery removed).

total capacitance after battery removal and insertion of dielectric = 2C + KC total charge = 2CV + CV. new potential ,

$V_{new} =\frac{Q_{total}}{C_{total}}= \frac{3CV}{(k+2)C} = \frac{3V}{K+2}$