The plates of a parallel plate capacitor are charged up to $100\, volt$. A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$. The dielectric constant of the plate is
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$\mathrm{Ed}=\mathrm{V}=(\mathrm{d}+1.6-2) \mathrm{E}+\frac{\mathrm{E}}{\mathrm{K}} \cdot 2$
$\frac{2}{{\text{K}}} = \frac{4}{{10}}\quad \boxed{{\text{K}} = 5}$
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