A) \[(4+k)\frac{C}{4}\]
B) \[(3+k)\frac{C}{4}\]
C) \[\frac{kC}{2}\]
D) \[\frac{kC}{4}\]
Correct Answer: B
Solution :
Capacitor with air as the dielectric has capacitance \[{{C}_{1}}=\frac{{{\varepsilon }_{0}}}{d}\left( \frac{3\,\,A}{4} \right)\,\,=\,\,\frac{3{{\varepsilon }_{0}}A}{4d}\] Similarly the capacitor with k as dielectric constant has capacitance \[{{C}_{2}}=\frac{{{\varepsilon }_{0}}k}{d}\left( \frac{A}{4} \right)\,\,=\,\,\frac{{{\varepsilon }_{0}}Ak}{4d}\] \[\because \,\,\,\,{{C}_{1}}\,\,and\,\,{{C}_{2}}\] are in parallel \[{{C}_{net}}=\,\,{{C}_{1}}\,\,+\,\,{{C}_{2}}\] \[=\,\,\,\,\frac{3{{\varepsilon }_{0}}4}{4d}+\frac{{{\varepsilon }_{0}}Ak}{4d}=\frac{{{\varepsilon }_{0}}A}{d}\,\left[ \frac{3}{4}+\frac{k}{4} \right]\] \[=\,\,\,\frac{C}{4}(3+k)\]
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