Q88 / 90 · JEE Main 2022 (25 Jul Shift 2) · Physics

Two parallel plate capacitors of capacity C and 3C 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.

Correct answer: 6

Solution

Figure

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.

Figure

Applying conservation of charge,

9CV'+3CV'=18CV+54CV

⇒12CV'=72CV⇒V'=6 V

Hence, the correct answer is 6.

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