When a certain capacitor carries charge of magnitude Q on each of its plates, it stores energy Ep. In order to store twice as much energy, how much charge should it have on its plates

2Q

When a capacitor carries some certain charge, the energy stored in the capacitor is its electric potential energy E. The magnitude of this potential energy is given by;

E  =            ------------(i)

Where;

q = charge between the plates of the capacitor

V = potential difference between the plates of the capacitor

From the question;

q = Q

E = Ep

Therefore, equation (i) becomes;

Ep =              ----------------(ii)

Make V subject of the formula in equation (ii)

V =

Now, when the energy is doubled i.e E = 2Ep, equation (i) becomes;

2Ep =

Substitute the value of V into the equation above;

2Ep = ()

Solve for q;

=

=

Therefore, the charge, when the energy stored is twice the originally stored energy, is twice the original charge. i.e 2Q

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