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  4. The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-

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Q. The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-

JEE MainJEE Main 2019Electrostatic Potential and Capacitance

Solution:

Total charge of the system = $CV + nCV$
$= (n + 1)CV$
After the insertion of dielectric of constant $K$
New potential (common)
$V_C = \frac{total \; charge}{total \; capacitance}$
$ = \frac{( n + 1) CV}{KC + nC} = \frac{(n + 1) V}{K + n}$

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