Answer:[tex]\sqrt{3}D[/tex]
Explanation:
Given
Diameter of Plates is D
distance between Plates is d
Energy Stored in the Plates is U
Suppose fixed Potential is V
Energy is given by
[tex]U=\frac{1}{2}CV^2[/tex]
where C=capacitance
[tex]C=\frac{\epsilon A}{d}[/tex]
where A=area of Plates
[tex]A=\frac{\pi D^2}{4}[/tex]
Thus [tex]C=\frac{\epsilon \cdot \pi \cdot D^2}{4d}[/tex]
Keeping all other factors as same
[tex]U\propto D^2----1[/tex]
For triple the Energy
[tex]3U\propto (D')^2-----2[/tex]
divide 1 and 2 we get
[tex]\frac{U}{3U}=\frac{D^2}{D'^2}[/tex]
[tex]D'=\sqrt{3}D[/tex]
Thus the diameter should be change to [tex]\sqrt{3}[/tex] times of original value
