,Energy storage in capacitors
A capacitor is capable of storing internal energy, due to charge begin moved across the voltage difference. For moving a small charge Dq across a capacitor, the change in potential energy is:
,
where q is the charge already on the capacitor. As a capacitor is charged from q=0, the first charges come on to the capacitor while it has little charge, and hence do little to the internal energy; while the last charges surmount the entire final voltage difference. With a little calculus one can show:
All three equations for the energy U, which are equivalent because C = q/V, will be useful.