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  4. An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V' . The dielectric constant K is

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Q. An uncharged parallel plate capacitor having a dielectric of constant $K$ is connected to a similar air cored parallel capacitor charged to a potential $V$. The two capacitors share charges and the common potential is $V' .$ The dielectric constant $K$ is

Electrostatic Potential and Capacitance

Solution:

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$V'=\frac{(K C)(0)+(C)(v)}{K C+C}$
$V'=\frac{C V}{K C+C}$
$K V'+V'=V$
$K V'=V'-V'$
$K=\frac{V-V'}{V'}$