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?
B
$$\dfrac{(n+1)V}{(K+n)}$$
Correct option is C. $$\dfrac{(n+1)V}{(K+n)}$$
After fully charging, battery is disconnected.
Total charge of the system$$=CV+nCV$$
$$=(n+1)CV$$
After the insertion of dielectric of constant K
New potential (common)
$$V_C=\dfrac{total charge}{total capacitance}$$
$$=\dfrac{(n+1)CV}{KC+nC}=\dfrac{(n+1)V}{K+n}$$.