Connecting a Charged to an Uncharged Capacitor
When a charged capacitor is connected to an uncharged capacitor charge flows from the charged to the uncharged capacitor until there is no net force on the charge carriers. This means that both capacitors are at the same potential, because if they were not, there would be an electric fieldand hence a force on the charge carriers of magnitudeand the charge carriers would move to equalize the potentials and reduce the electric field and hence the force, eventually to zero.
Of course, as charge flows from one capacitor to the other, the total charge is conserved.
In the diagram above, when switch is closed chraged flows from the top capacitor to the bottom. When charge has stopped flowing,
Also, because the potentials are equal(1)
Suppose then that the capacitor at top left is initially charged to potential ofand that it has capacitanceand is then connected to a capacitance
Initiallystores a charge
From (1) (4)
Sub (4) into (1) to get
Now usefor either capacitor to findUsing it for (2) gives