Question

An ideal parallel-plate capacitor having circular plates of diameter D that are a distance d apart stores energy U when it is connected across a fixed potential difference. If you want to triple the amount of energy stored in this capacitor by changing only the size of its plates, the diameter should be changed to______________.

Answer 1

Answer:$\sqrt{3}D$

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

$U=\frac{1}{2}CV^2$

where C=capacitance

$C=\frac{\epsilon A}{d}$

where A=area of Plates

$A=\frac{\pi D^2}{4}$

Thus $C=\frac{\epsilon \cdot \pi \cdot D^2}{4d}$

Keeping all other factors as same

$U\propto D^2----1$

For triple the Energy

$3U\propto (D')^2-----2$

divide 1 and 2 we get

$\frac{U}{3U}=\frac{D^2}{D'^2}$

$D'=\sqrt{3}D$

Thus the diameter should be change to $\sqrt{3}$ times of original value