Question

Two parallel plates of area A are separated by two different dielectrics as shown in figure. The net capacitance is

• A. $\frac{\epsilon_{0}A}{2d}$
• B. $\frac{\epsilon_{0}A}{d}$
• C. $\frac{3\epsilon_{0}A}{d}$
• D. $\frac{4\epsilon_{0}A}{3d}$

Hint:

Two parallel plates of area A are separated by two different dielectrics as shown in figure. The net capacitance is \includegraphics[width=0.5\linewidth]49phy.png \labelfig:placeholder

Answer 1

The Correct Option is D

Step 1: Formula
Net capacitance for dielectrics in series: $C = \frac{\epsilon_{0}A}{\frac{d_{1}}{K_{1}} + \frac{d_{2}}{K_{2}}}$.
Step 2: Values
$d_{1} = d/2, K_{1} = 1$ and $d_{2} = d/2, K_{2} = 2$.
Step 3: Calculation
$C = \frac{\epsilon_{0}A}{\frac{d}{2}(\frac{1}{1} + \frac{1}{2})} = \frac{\epsilon_{0}A}{\frac{d}{2}(\frac{3}{2})} = \frac{4\epsilon_{0}A}{3d}$.
Final Answer: (d)