Two metallic plates form a parallel plate capacitor. The distance between the plates is $'d'.$ A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor $?$
JEE MAIN 2022, Medium
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$C _{1}=\frac{\epsilon_{0} A }{ d }$
$C _{2}=\frac{\epsilon_{0} A }{\frac{ d }{2}+\frac{ d / 2}{\propto}}=\frac{2 \epsilon_{0} A }{ d }$
$\frac{ C _{2}}{ C _{1}}=\frac{2}{1}$
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