A) \[(K+3)\frac{C}{4}\]
B) \[(K+2)\frac{C}{4}\]
C) \[(K+1)\frac{C}{4}\]
D) \[\frac{KC}{4}\]
Correct Answer: A
Solution :
Capacitance of a capacitor with dielectric as air \[{{C}_{1}}=\frac{{{\varepsilon }_{0}}}{d}\left( \frac{3A}{4} \right)=\frac{3{{\varepsilon }_{0}}A}{4d}\] Similarly, the capacitance of a capacitor with dielectric constant K \[{{C}_{2}}=\frac{{{\varepsilon }_{0}}K}{d}\left( \frac{A}{4} \right)=\frac{{{\varepsilon }_{0}}AK}{4d}\] \[{{C}_{1}}\] and \[{{C}_{2}}\] are in parallel \[{{C}_{net}}={{C}_{1}}+{{C}_{2}}\] \[=\frac{3{{\varepsilon }_{0}}A}{4d}+\frac{{{\varepsilon }_{0}}AK}{4d}=\frac{C}{A}(K+3).\]
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