Question

Two identical metal plates, separated by a distance d form a parallel plate capacitor. A metal sheet of thickness$\frac{d}{2}$ of the same area as that of either plate, is inserted between the plates. The ratio of the capacitance's after the insertion of the sheet to that before insertion is:

• A. $\sqrt{2}:1$
• B. 2 :1
• C. 1:1
• D. $1:\sqrt{2}$

Answer 1

The correct option is B 2 :1

The effective capacitance of above capacitance is series combination of $\frac{{4ϵ}_{0}A}{d}$ and $\frac{{4ϵ}_{0}A}{d}$

$\Rightarrow \frac{1}{C_q}=\frac{d}{4{ϵ}_{0}A}+\frac{d}{4{ϵ}_{0}A}$

$\Rightarrow C_{eff}=\frac{2{ϵ}_{0}A}{d}$

$\frac{C_2}{C_1}=\frac{\frac{2{ϵ}_{0}A}{d}}{\frac{{ϵ}_{0}A}{d}}=2:1$