Question

A parallel plate capacitor has two layers of dielectric as shown in figure. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is:

• A. $\frac{4}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is D $\frac{3}{2}$

$C_1=\frac{K_1{ϵ}_{0}A}{d};C_2=\frac{K_2{ϵ}_{0}A}{2d}$
$q=C_1{V}_1=C_2{V}_2;\frac{V_1}{V_2}=\frac{C_2}{C_1}=\frac{K_2}{2K_1}=\frac{6}{2\times 2}$
$\frac{V_1}{V_2}=\frac{3}{2}$