Two parallel plate capacitors of capacity C and 3 C are connected in parallel combination and charged to a potential difference 18 V . The battery is then disconnected and the space between the plates

Question

Two parallel plate capacitors of capacity C and 3 C are connected in parallel combination and charged to a potential difference 18 V . 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 .

TestHub · Accepted Answer

The charge on the capacitor is given by $q = C V$ .
Initial charge on $C = 18 C V$
And initial charge on $3 C = 54 C V$
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,
$9 C V^{'} + 3 C V^{'} = 18 C V + 54 C V$
$\Rightarrow 12 C V^{'} = 72 C V \Rightarrow V^{'} = 6 V$

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