Question

A parallel plane condenser is filled with two dielectrics as shown in figure. Area of each plate is A in m2 and the separation is d metre. The dielectric constants are ${{K}_{1}}$ and ${{K}_{2}}$ respectively. Its capacitance in farad will be:

• A. $\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)$
• B. $\frac{2 \in_{0} A }{ d }\left(\frac{ K _{1} K _{2}}{ K _{1}+ K _{2}}\right)$
• C. $\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{2{{K}_{1}}{{K}_{2}}} \right)$
• D. $\frac{{{\varepsilon }_{0}}A{{K}_{1}}+{{K}_{2}}}{2({{d}_{2}}{{K}_{1}}+{{d}_{1}}{{K}_{2}})}$

Answer 1

Answer: (B)

$\frac{2 \in_{0} A }{ d }\left(\frac{ K _{1} K _{2}}{ K _{1}+ K _{2}}\right)$

Answer 2

From the formula $C=\frac{{{\varepsilon }_{0}}A}{\frac{1}{{{K}_{1}}}+\frac{1}{{{K}_{2}}}}=\frac{{{\varepsilon }_{0}}A}{t}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)$ $=\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)$