# 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 capacitors . The new potential difference of the combined system is :Option 1)$\frac{nV}{K+n}$  Option 2)$V$Option 3)$\frac{V}{K+n}$  Option 4)$\frac{(n+1)V}{(K+n)}$

$\left ( C_{eq} \right )_{initially}={n}C+C=(n+1)C$

$Q=(n+1)C\:V$

Q should be conserved after removal of battery

$\Rightarrow (C_{eq})_{final}=nC+kC=(n+k)C$

$\Rightarrow (n+k)C\:\:V_{final }=(n+1)C\:V$

$\Rightarrow \:V_{final }=\frac{n+1}{n+k}\:V$

Option 1)

$\frac{nV}{K+n}$

Option 2)

$V$

Option 3)

$\frac{V}{K+n}$

Option 4)

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

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