There are two identical capacitors, the first one is uncharged and filled with a dielectric constant K while the other one is charged to potential V having air between its plates. If two capacitors are joined end to end, the common potential will be

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$\frac{V}{K - 1}$

$\frac{K V}{V + 1}$

$\frac{K V}{K - 1}$

$\frac{V}{K + 1}$

answer is D.

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Detailed Solution

Initially,

$Q = C V$ for the charged capacitor.

After the capacitors are connected,

$Q' = K C V'$ for the capacitor with a dielectric constant of K

and $Q " = C V'$ for the capacitor with air

$C V = K C V' + C V'$

$V' = \frac{V}{K + 1}$

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