# Current on both sides of a capacitor

When a capacitor is connected to a DC circuit, what ensures that the current on both sides of the capacitor is the same? When charges arrive at one end of the capacitor they stop moving; presumably they give their kinetic energy to charges on the other side of the capacitor so they can leave. How exactly does this transfer of energy occur?

• That the current on both leads of a capacitor is the same is an approximation that characterizes lumped two-poles. In general, however, a conductive structure with the typical shape of a capacitor does not conserve current this way if it can radiate electromagnetic waves into free space, but that's very hard to calculate, so for technical applications we assume that the capacitor is a self-contained element, rather than the combination of two antennas. This works because we can often simplify the problem to a pure displacement current between the two plates and neglect the external fields. Jul 12 '15 at 21:44
• Sorry, what are lumped two-poles? Jul 12 '15 at 21:48
• A lumped two-pole is the general circuit element with two connections (like resistors, capacitors, inductors, diodes etc.), for which we can neglect the internal structure and the relative geometry of the physical component in relationship to other components, wires, etc.. We can describe them with a low frequency current/voltage relationship like Ohm's law or the capacitor or inductor formulas. For frequencies with wavelengths of the size of the physical component this is not correct, any longer, and we need refined models that take electromagnetic radiation into account. Jul 12 '15 at 21:53