Question

A $1.0$cm thick plate of dielectric material is placed midway between two copper as shown in figure. If the capacity before introducing the dielectric is $C_1$ an after introducing dielectric $C_2$. ($K$ is dielectric constant).

• A. $C_1/C_2=\frac{2}{2+1/k}$
• B. $C_1/C_2=\frac{1}{3}(2+k)$
• C. $C_1/C_2=\frac{1}{3}(\frac{2}{k}+1)$
• D. $C_1/C_2=\frac{1}{3}(\frac{1}{k}+2)$

Answer 1

The correct option is D $C_1/C_2=\frac{1}{3}(\frac{1}{k}+2)$

We know,

$C_1=\frac{{ϵ}_{0}A}{d}$

$C_2=\frac{{ϵ}_{0}A}{d-t(1-\frac{1}{k})}$

$\Rightarrow \frac{C_1}{C_2}=\frac{d-t(1-\frac{1}{k})}{d}$

$\Rightarrow \frac{C_1}{C_2}=\frac{3-1(1-\frac{1}{k})}{3}$

$=1-\frac{1}{3}(1-\frac{1}{k})$

$=\frac{2}{3}\frac{1}{3k}=\frac{1}{3}(2+\frac{1}{k})$