Two metal plates each of area ' $A$ ' form a parallel plate capacitor with air in between the plates. The…
Two metal plates each of area ' $A$ ' form a parallel plate capacitor with air in between the plates. The distance between the plates is ' $d$ '. A metal plate of thickness $\frac{d}{2}$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$, then $\frac{C^{\prime}}{C}$ is
$4$
$2$
$6$
$1$
Solution
We knows capacitance $C=\frac{\varepsilon_0 A}{d}$
When plate is inserted
$
\begin{gathered}
C^{\prime}=\frac{\varepsilon_0 A}{d-\frac{d}{2}}=\frac{2 \varepsilon_0 A}{d} \\
\frac{C^{\prime}}{C}=\frac{2}{1}
\end{gathered}
$
