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 from P to Q is

• A. $\frac{4}{3}$
• B. $\frac{1}{2}$
• C. $\frac{5}{2}$
• D. $\frac{3}{2}$

Answer 1

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

Capacitance of left section will be

$C_1=\frac{K_1{ϵ}_{o}A}{d}=\frac{2{ϵ}_{o}A}{d}=2C_o$ (say)

Similarly, capacitance of right section is

$C_2=\frac{6{ϵ}_{o}A}{2d}=3C_o$

Since charge on each section will be same because they are in series, so,

$V\propto \frac{1}{C}(\because Q=CV)$

$\therefore \frac{V_1}{V_2}=\frac{C_2}{C_1}=\frac{3C_o}{2C_o}=\frac{3}{2}$

Hence, option $\left(d\right)$ is correct.