A) \[\frac{C}{2}\]
B) \[\frac{3C}{4}\]
C) \[4C\]
D) \[2C\]
Correct Answer: D
Solution :
Given: Initial capacitance \[=C\] Initial thickness of the sheet \[{{t}_{1}}=d\](where d is the separation between plates) Final thickness of sheet \[{{t}_{2}}=\frac{d}{2}\] The capacitance of a parallel plate capacitor is given by \[C=\frac{{{E}_{0}}A}{d}\propto \frac{1}{d}\] Hence \[\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{{{d}_{2}}}{{{d}_{1}}}=\frac{\frac{d}{2}}{d}=\frac{1}{2}\](where \[{{C}_{2}}\]is the new capacitance of a capacitor) Hence, \[{{C}_{2}}=2{{C}_{1}}=2C\]
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