Question

The capacitance of a parallel plate capacitor when a very thin metallic sheet is placed in the space between the plates, parallel to the plates, will:

• A. increase
• B. decrease
• C. Remain same
• D. Nothing can be said

Answer 1

The correct option is A increase

If a then plate of thickness $d$ is introduced in a parallelogram plate capacitor then the interior of the capacitor a divided into two parts

a) a part of thickness $t$ will permilturty $ϵ$ of the thin plate

b) a part of thickness $(d-t)$ with permilturty ${ϵ}_0$ of air

$\therefore V=\frac{Q}{A}[\frac{t}{ϵ}+\frac{d-t}{{ϵ}_0}]$

$\Rightarrow e=\frac{Q}{V}=\frac{{ϵ}_{0}A}{d-t(1-\frac{1}{K})}$

where $ϵ=K{ϵ}_0$

As the dieledtrie constant of a sheet $K>1$ therefore

$e$ increase upon the introduction of the thin plate