Question

A capacitor is formed by two square metal plates each of edge $a=10\text{cm}$ separated by a distance $d=7\text{mm}$. Dielectrics of dielectric constant $K_1=8$ and $K_2=4$ are filled in the gap as shown in figure, what is the capacitance of this system? $(\ln 2=0.7)$

• A. $35.4\text{pF}$
  
• B. $70.8\text{pF}$
• C. $141.6\text{pF}$
  
• D. $78\text{pF}$

Answer 1

The correct option is B $70.8\text{pF}$

We know that for an arrangement shown in the question

Capacitance of the system is given by, $C=\frac{{\epsilon }_0{a}^2{K}_1{K}_2}{(K_1-K_2)d}\ln \frac{K_1}{K_2}$

We have the values of corresponding variables as,
$a=0.1\text{m}$
$d=7\times {10}^{-3}$
$K_1=8$
$K_2=4$

Substituting the given data we get, $C=\frac{8.85\times {10}^{-12}\times 0.1\times 8\times 4}{(8-4)7\times {10}^{-3}}\ln \frac{8}{4}$

$\therefore C=70.8\text{pF}$

Hence, option (b) is the correct answer.