Question

A parallel-plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. The sheet remains parallel to the plates of the capacitor. It's capacitance will:

• A. Increase
• B. Decrease
• C. Remains the same
• D. Becomes infinite

Answer 1

The correct option is C Remains the same

We know that $C=\frac{{\epsilon }_{o}A}{d}$,

So,

$\begin{array}{c}{C}_1=\frac{A{\epsilon }_o}{x}\\ C_2=\frac{A{\epsilon }_o}{d-x}\\ C_{eq}=\frac{\frac{A{\epsilon }_o}{x}.\frac{A{\epsilon }_o}{d-x}}{\frac{A{\epsilon }_o}{x}+\frac{A{\epsilon }_o}{d-x}}\\ C_{eq}=\frac{{\epsilon }_{o}A}{d}\\ Henc,Cremainsunchanged.\end{array}$