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  4. 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

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Q. 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______ $V$

JEE MainJEE Main 2022Electrostatic Potential and Capacitance

Solution:

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Initial charge on $C =18\, CV$
initial charge on $3 C =54 \,CV$
Let final common potential difference $= V ^{\prime}$
$9\, CV ^{\prime}+3 \,CV ^{\prime}=18 \,CV +54 \,CV$
$\Rightarrow 12\, CV ^{\prime}=72 \,CV \Rightarrow V ^{\prime}=6\, V$