Question

Find equivalent capacitance of system if plate area is $A$.
[Dielectric slab of constant $2K$ and $K$ are of same volume and half of the volume of the slab of constant $3K$.]

• A. $\frac{5{ϵ}_{0}AK}{d}$
• B. $\frac{13}{6}\frac{{ϵ}_{0}AK}{d}$
• C. $\frac{6{ϵ}_{0}AK}{d}$
• D. $\frac{15}{7}\frac{{ϵ}_{0}AK}{d}$

Answer 1

The correct option is B $\frac{13}{6}\frac{{ϵ}_{0}AK}{d}$


$C_1=\frac{{ϵ}_{0}AK}{2\frac{d}{2}}=\frac{{ϵ}_{0}AK}{d}$
$C_2=\frac{{ϵ}_{0}A2K}{2\frac{d}{2}}=\frac{2{ϵ}_{0}AK}{d}$
$C_3=\frac{{ϵ}_{0}A3K}{2\times \frac{d}{2}}=\frac{3{ϵ}_{0}AK}{d}$


$C_4=\frac{C_3}{2}=\frac{3}{2}\frac{{ϵ}_{0}AK}{d}\&C_5=\frac{C_1{C}_2}{C_1+C_2}$
$C_{eq}=C_4+C_5=\frac{3}{2}\frac{{ϵ}_{0}AK}{d}+\frac{2}{3}\frac{{ϵ}_{0}AK}{d}$
$C_{eq}=\frac{13}{6}\frac{{ϵ}_{0}AK}{d}$