Question

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor carries a charge Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will be...a) unchangedb) quarteredc) halvedd) doublede) quadrupled

Answer 1

Answer:

C) Half  

Explanation:

Given that

Area of plates =A

Distance between plates = d

The charge on the capacitor = C

We know that capacitance C is given as

$C=\dfrac{\varepsilon _0A}{d}$

The stored energy U is given as

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

When distance gets double ,d ' = 2 d

The value of new capacitance

$C'=\dfrac{\varepsilon _0A}{d'}$

$C'=\dfrac{\varepsilon _0A}{2d}$

$C'=\dfrac{C}{2}$

New stored energy U'

$U'=\dfrac{1}{2}C'V^2$

$U'=\dfrac{1}{2}\times \dfrac{C}{2}\times V^2$

$U'=\dfrac{1}{2}\times \dfrac{C}{2}\times V^2$

$U'=\dfrac{U}{2}$

Therefore the stored energy get half .

C) Half