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  4. Two parallel plate capacitors of capacitance C and 2C are connected in parallel and charged to a potential difference V0. The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material of dielectric constant 2 . The potential difference across the capacitors now becomes

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Q. Two parallel plate capacitors of capacitance $C \, and \, 2C$ are connected in parallel and charged to a potential difference $V_{0}.$ The battery is then disconnected and the region between the plates of the capacitor $C$ is completely filled with a material of dielectric constant $2$ . The potential difference across the capacitors now becomes

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
Initial state
Solution
As both capacitors have the same capacitance total charge $= C V_{0} + 2 C V_{0}$
$= 3 C V_{0}$
It will be divided equaly so $q_{1} = q_{2} = \frac{3 C V_{0}}{2}$ & potential $= \frac{q}{C} = \frac{\left(\right. \frac{3 C V_{0}}{2} \left.\right)}{2 C} = \frac{3 V_{0}}{4}$