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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