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Q. There are two identical capacitors, the first one is uncharged and filled with a dielectric of constant $K$ while the other one is charged to potential $V$ having air between its plates. If two capacitors are joined end to end, the common potential will be

Electrostatic Potential and Capacitance

Solution:

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$V'=\frac{K C(0)+C V}{K C+C}$
$V'=\frac{C V}{C(I+K)}$
$V'=\frac{V}{l+K}$