Question

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

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

Answer 1

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

Let $E_1$ be electric field inside dielectric of constant $K_1$ and
$E_2$ be electric field inside dielectric of constant $K_2$

Potential difference across dielectrics is
$\Delta V_1=E_{1}d....\left(1\right)$
$\Delta V_2=E_{2}2d....\left(2\right)$
Dividing equations $\left(1\right)/\left(2\right)$
$\frac{\Delta V_1}{\Delta V_2}=\frac{E_1}{2E_2}=\frac{1}{2}\times \frac{K_2}{K_1}$
$[\because \frac{E_1}{E_2}=\frac{K_2}{K_1}]$
$\frac{\Delta V_1}{\Delta V_2}=\frac{6}{2\times 2}=\frac{3}{2}$