A) remain the same
B) increase 4 times
C) increase 2 times
D) decrease 2 times
Correct Answer: B
Solution :
Key-Idea: In order to obtain high capacitance, plats of large area should be taken and kept close to each other. The capacitance of a parallel plate capacitor of plate area A and the distance \[d\], between the plated is given by \[C=\frac{K{{\varepsilon }_{o}}A}{d}\] Given, \[{{d}_{1}}=d,\,\,{{d}_{2}}=\frac{d}{2},\,{{K}_{1}}=K,\,\,{{K}_{2}}=2K\] \[\therefore \] \[\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{{{K}_{1}}}{{{d}_{1}}}\times \frac{{{d}_{2}}}{{{K}_{2}}}\] \[=\frac{K}{d}\times \frac{d}{2\times 2\,K}\] \[\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{1}{4}\] \[\Rightarrow \] \[{{C}_{2}}=4\,{{C}_{1}}\] Hence, Capacitance increases four times.
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