Question 91 of 180

Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a potential difference $18V$. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$. The final potential difference across the combination of capacitors will be _____ $V$.

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Answer: 6

The charge on the capacitor is given by $q=CV$.
Initial charge on $C=18CV$
And initial charge on $3C=54CV$
Let final common potential difference $={V}^{'}$
When a dielectric of dielectric constant $k$ is introduced between the plates of the capacitor the capacitance becomes $k$ times.

Applying conservation of charge,
$9C{V}^{'}+3C{V}^{'}=18CV+54CV$
$\Rightarrow 12C{V}^{'}=72CV\Rightarrow {V}^{'}=6V$