question_answer

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

A)  \[4/3\]                         

B)  \[1/2\]

C)  \[1/3\]                         

D)  \[3/2\]

Correct Answer: D

Solution :

Suppose electric field in dielectric are \[{{E}_{1}}\] and \[{{E}_{2}}\]                 \[\Rightarrow \]               \[\frac{\Delta {{V}_{1}}}{\Delta {{V}_{2}}}=\frac{{{E}_{1}}d}{{{E}_{2}}2d}=\frac{3}{2}\]    \[\left( \because \,\,\frac{{{E}_{1}}}{{{\varepsilon }_{1}}}=\frac{{{K}_{2}}}{{{K}_{1}}}=3 \right)\]