Question

A parallel plate capacitor with air as medium between the plates has a capacitance of $10\mu \text{F}$. The capacitor is divided into two equal halves and filled with two media having dielectric constant $K_1=2$ and $K_2=4$. The capacitance of the system will be

• A. $10\mu \text{F}$
• B. $20\mu \text{F}$
• C. $30\mu \text{F}$
• D. $40\mu \text{F}$

Answer 1

The correct option is C $30\mu \text{F}$

Let $A$ be the area of plate and $d$ be the separation between both plates.

So, capacitance will be

$C=\frac{{ϵ}_{o}A}{d}=10\mu \text{F}$

Since, the given arrangement is in parallel combination so equivalent capacitance will be

$C_{eq}=C_1+C_2=\frac{K_1{ϵ}_o{A}_1}{d}+\frac{K_2{ϵ}_o{A}_2}{d}$

$\Rightarrow C_{eq}=\frac{2\times {ϵ}_o\times A/2}{d}+\frac{4\times {ϵ}_o\times A/2}{d}$

$\Rightarrow C_{eq}=\frac{{ϵ}_{o}A}{d}+\frac{2{ϵ}_{o}A}{d}=10+(2\times 10)$
$[\because C=\frac{{ϵ}_{o}A}{d}=10\mu \text{F}]$

$\therefore C_{eq}=30\mu \text{F}$

Therefore, option $\left(c\right)$ is correct.