A) \[\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{{{K}_{1}}{{K}_{2}}} \right)\]
B) \[\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}} \right)\]
C) \[\frac{{{\varepsilon }_{0}}A}{d}\left( \frac{{{K}_{1}}+{{K}_{2}}}{2{{K}_{1}}{{K}_{2}}} \right)\]
D) \[\frac{{{\varepsilon }_{0}}A{{K}_{1}}{{K}_{2}}}{2\,({{d}_{2}}{{K}_{1}}+{{d}_{1}}{{K}_{2}})}\]
Correct Answer: B
Solution :
This is equivalent to the series combination of two capacitor \[{{C}_{equivalent}}=\frac{{{\varepsilon }_{0}}A}{\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}}=\frac{{{\varepsilon }_{0}}A}{t}\left( \frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}} \right)\] \[=\frac{2{{\varepsilon }_{0}}A}{d}\left( \frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}} \right)\]You need to login to perform this action.
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