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  4. Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness ( 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 ?

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Q. 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 MainJEE Main 2022Electrostatic Potential and Capacitance

Solution:

$C _{1}=\frac{\epsilon_{0} A }{ d }$
$C _{2}=\frac{\epsilon_{0} A }{\frac{ d }{2}+\frac{ d / 2}{\propto}}=\frac{2 \epsilon_{0} A }{ d }$
$\frac{ C _{2}}{ C _{1}}=\frac{2}{1}$