Question

Two metal plates form a parallel plate condenser. The distance between the plates is $d.$ A metal plate of thickness $\frac{d}{2}$ and of the same area is inserted completely between the plates. The ratio of capacitance's in the two cases (later to initial)

• A. $2:1$
• B. $1:2$
• C. $1:1$
• D. $1:4$

Answer 1

The correct option is C $1:1$

$C=\frac{{ϵ}_{0}A}{d}$

$C^{\prime }=\frac{{ϵ}_{0}A}{d-t+\frac{t}{k}}$

After inserting metal plate of $\frac{d}{2}$ thickness; $t=\frac{d}{2},k=1$

$\Rightarrow C^{\prime }=\frac{{ϵ}_{0}A}{d-\frac{d}{2}+\frac{d}{2}}$

$C^{\prime }=\frac{{ϵ}_{0}A}{d}=C$

Thus, ratio = $1:1$