The parallel combination of two air filled parallel plate capacitors of capacitance

Question:

The parallel combination of two air filled parallel plate capacitors of capacitance $\mathrm{C}$ and $n \mathrm{C}$ 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 $\mathrm{K}$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is:

  1. (1) $\frac{n \mathrm{~V}}{\mathrm{~K}+n}$

  2. (2) $\mathrm{V}$

  3. (3) $\frac{\mathrm{V}}{\mathrm{K}+n}$

  4. (4) $\frac{(n+1) \mathrm{V}}{(\mathrm{K}+n)}$

Correct Option: , 4

Solution:

(4) $V^{\prime}=\frac{C V+(n C) V}{k C+n C}$

$\frac{(n+1) V}{k+n}$

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