A) \[{{K}_{1}}+{{K}_{2}}\]
B) \[\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}-{{K}_{2}}}\]
C) \[\frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}}\]
D) \[\frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
Correct Answer: D
Solution :
\[{{C}_{A}}=\frac{{{K}_{1}}{{\varepsilon }_{0}}A}{d/2},\,{{C}_{B}}=\frac{{{K}_{2}}{{\varepsilon }_{0}}A}{d/2}\] \ \[{{C}_{eq}}=\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\] \[=\frac{{{C}_{A}}{{C}_{B}}}{{{C}_{A}}+{{C}_{B}}}=\left( \frac{2{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\,\frac{{{\varepsilon }_{0}}A}{d}\] \[\left( \because \,\,c=\frac{{{\varepsilon }_{0}}A}{d} \right)\]You need to login to perform this action.
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