A Parallel Plate Capacitor Has Capacitance C. If It Is Equally Filled The Parallel Of Materials Of Dielectric Constant K1 And K2 Its Capacity Becomes C1 . The Ratio Of C1 And C Is

\( C_{A} = \frac{K_{1}\epsilon _{0}A}{\frac{d}{2}} \) \( C_{B} = \frac{K_{2}\epsilon _{0}A}{\frac{d}{2}} \)

Capacitance,

\( C_{eq} = \frac{C_{1}}{C_{2}} \) \( \Rightarrow \frac{2K_{1}K_{2}}{K_{1} + K_{2}} \) \( \Rightarrow \frac{C_{A}C_{B}}{C_{A} + C_{B}} = (\frac{2K_{1}K_{2}}{K_{1} + K_{2}}) \frac{\epsilon _{0}A}{d} \)

Since e = \( \frac{\epsilon _{0}A}{d} \)

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