Question
A parallel plate capacitor has capacitance $C$. If it is equally filled with parallel layers of materials of dielectric constants $K_1$ and $K_2$ its capacity becomes $C_1$. The ratio of $C_1$ to $C$ is
✓
Answer
(d)${C_A} = \frac{{{K_1}{\varepsilon _0}A}}{{d/2}},\,{C_B} = \frac{{{K_2}{\varepsilon _0}A}}{{d/2}}$
${C_{eq}} = \frac{{{C_1}}}{{{C_2}}} = \frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
$ = \frac{{{C_A}{C_B}}}{{{C_A} + {C_B}}} = \left( {\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}} \right)\,\frac{{{\varepsilon _0}A}}{d}$ $\left( {\,\,c = \frac{{{\varepsilon _0}A}}{d}} \right)$
${C_{eq}} = \frac{{{C_1}}}{{{C_2}}} = \frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}$
$ = \frac{{{C_A}{C_B}}}{{{C_A} + {C_B}}} = \left( {\frac{{2{K_1}{K_2}}}{{{K_1} + {K_2}}}} \right)\,\frac{{{\varepsilon _0}A}}{d}$ $\left( {\,\,c = \frac{{{\varepsilon _0}A}}{d}} \right)$
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