A) \[\left( {{k}_{1}}+\,{{k}_{2}} \right)/2\]
B) \[2{{k}_{1}}{{k}_{2}}/\left( {{k}_{1}}+\,{{k}_{2}} \right)\]
C) \[{{k}_{1}}{{k}_{2}}/\left( {{k}_{1}}+\,{{k}_{2}} \right)\]
D) None of these
Correct Answer: B
Solution :
Capacitance of a capacitor is given by \[C=\frac{{{\varepsilon }_{0}}kA}{d}\] According to question, \[{{C}_{1}}\,\,=\,\,\frac{{{k}_{1}}{{\varepsilon }_{0}}A}{d/2}\] \[=\frac{2{{k}_{1}}{{\varepsilon }_{0}}A}{d}\] Similarly, \[{{C}_{2}}\,\,=\,\,\frac{2{{k}_{2}}{{\varepsilon }_{0}}A}{d}\] Now, these capacitor are in series \[C=\frac{{{C}_{1}}{{C}_{2}}}{({{C}_{1}}+{{C}_{2}})}\] Also, \[C=\frac{{{C}_{1}}{{C}_{2}}}{({{C}_{1}}+{{C}_{2}})}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{k}_{eq}}=\frac{2{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]You need to login to perform this action.
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