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 share the charge and the common potential is $V'$. The dielectric constant $K$ is
Medium
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$\mathrm{V}^{\prime}=\frac{\mathrm{C}_{1} \mathrm{V}_{1}+\mathrm{C}_{2} \mathrm{V}_{2}}{\mathrm{C}_{1}+\mathrm{C}_{2}}=\frac{\mathrm{CV}+\mathrm{KC0}}{\mathrm{C}(\mathrm{K}+1)}$
$\mathrm{V}^{\prime}=\frac{\mathrm{V}}{\mathrm{K}+1} \Rightarrow \mathrm{K}=\frac{\mathrm{V}-\mathrm{V}^{\prime}}{\mathrm{V}^{\prime}}$
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