Question:

The parallel combination of two air-filled parallel plate capacitors of capacitance C and NC is connected to a battery of voltage V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is?

VK+n

nVK+n

(n+1)V/(K+n)

Correct option is (n+1)V/(K+n)

After fully charging, the battery is disconnected.
Total charge of the system = CV + nCV = (n+1)CV

After the insertion of dielectric of constant K
New potential (common) V_C = total charge / total capacitance = (n+1)CV / (KC + nC) = (n+1)V/(K+n).