Question

Two materials of dielectric constant $ {{k}_{1}} $ and $ {{k}_{2}} $ are filled between two parallel plates of a capacitor as shown in fig. The capacities of capacitor is :

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

Answer 1

Answer: (D)

Capacitance of the first capacitor $ {{C}_{1}}=\frac{{{\varepsilon }_{0}}A{{K}_{1}}}{d} $ Capacitance of the second capacitor $ {{C}_{2}}=\frac{{{\varepsilon }_{0}}A{{K}_{2}}}{d} $ As the two capacitors are connected in a parallel combination. Therefore, the net capacity will be $ C={{C}_{1}}+{{C}_{2}}=\frac{{{\varepsilon }_{0}}{{K}_{1}}A}{d}+\frac{{{\varepsilon }_{0}}{{K}_{2}}A}{d} $ $ =\frac{A{{\varepsilon }_{0}}}{d}({{K}_{1}}+{{K}_{2}}) $