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) \[\frac{A{{\varepsilon }_{0}}({{k}_{1}}+{{k}_{2}})}{d}\]
Correct Answer: D
Solution :
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 \[C={{C}_{1}}+{{C}_{2}}=\frac{{{\varepsilon }_{0}}{{K}_{1}}A}{d}+\frac{{{\varepsilon }_{0}}{{K}_{2}}A}{d}\] \[=\frac{A{{\varepsilon }_{0}}}{d}({{K}_{1}}+{{K}_{2}})\]
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