The distance between two plates of a capacitor is $d$ and its capacitance is $C _1$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2 d }{3}$ and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes $C _2$. The ratio $\frac{ C _2}{ C _1}$ is:
JEE MAIN 2023, Medium
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$K _{\text {metal sheet }}=\infty, t =\frac{2 d }{3}$
$C _1=\frac{\in_0 A }{ d }$
$C _2=\frac{\in_0 A }{ d - t +\frac{ t }{ k }}=\frac{\in_0 A }{ d -\frac{2 d }{3}+0}=3 C _1$
$\frac{ C _2}{ C _1}=3$
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