Question

A parallel plate capacitor is of area $6c{m}^2$and a separation $3mm$. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant $K_1=10,K_2=12$ and $K_3=14$. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

• A. $34$
• B. $12$
• C. $4$
• D. $14$

Answer 1

The correct option is B

$12$

Step 1: Given Data and drawing the diagram

Area of plates, $A=6c{m}^2$

The separation between plates, $d=3mm$

Dielectric constant, $$\begin{gathered} K_1=10, \\ {K}_2=12, \\ {K}_3=14 \end{gathered}$$

Step 2: Find the dielectric constant of a material which when fully inserted into the above capacitor

Let $K$ be the dielectric constant of the material used.

$$\begin{gathered} \frac{10{\epsilon }_0{\displaystyle \frac{A}{3}}}{d}+\frac{12{\epsilon }_0{\displaystyle \frac{A}{3}}}{d}+\frac{14{\epsilon }_0{\displaystyle \frac{A}{3}}}{d}=\frac{K{\epsilon }_0{\displaystyle A}}{d} \\ \Rightarrow K=12 \end{gathered}$$

Hence, option B is correct.