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I have a question about capacitors which is bothering me.

Why do capacitors obey KCL?

A fundamental fact used in electrical engineering is that in a circuit if charge enters in one terminal of a capacitor, an equal amount leaves the other terminal. It's not clear to me why this is the case?

For a capacitor with one terminal left floating it is possible to insert charge into the other terminal without producing a charge leaving the floating terminal. Why is it KCL is obeyed under the normal operation of a capacitor instead of this behavior occurring?

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  • $\begingroup$ What is "a capacitor with one terminal left floating"? And where are you getting charge to insert into it under normal operation? $\endgroup$ – A. C. A. C. Nov 14 '17 at 20:20
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Imagine what would happen if you have an unbalanced capacitor, with just one side charged. The capacitor has a net charge, and so tends to draw the opposite polarity towards both of its terminals. This tends to balance out the charges, usually very quickly.

In a circuit, in principle it is possible with an idealized current source to inject a current into one end of a capacitor. But if the other end of the capacitor is connected to anything else, the charges on that end experience a large force that pushes those charges out that end. And that eventually finds its way to the other end of your current source.

A capacitor with one end disconnected does not act like an ordinary capacitor. If you inject current into it, it is acting as a capacitor with the ground as the other plate. And indeed, charge is being drawn from ground to pump into the capacitor, so even there the capacitor is still balanced.

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  • $\begingroup$ Okay but ignoring this hypothetical scenario, why exactly do capacitors in normal operation obey KCL? It's not clear to me why charge can't just accumulate on one end, in a greater amount then what's lost on the other end. $\endgroup$ – FourierFlux Nov 15 '17 at 5:17
  • $\begingroup$ @FourierFlux The first paragraph of my answer. Any process that you expect might cause an imbalance in charge (i.e. KCL violation) would quickly be cancelled out by the electric fields this imbalance created (restoring KCL). $\endgroup$ – Chris Nov 15 '17 at 5:20
  • $\begingroup$ The capacitor has an imbalance of charge though, even if the total sum of charge equals 0 out there is still a build up of charge on one plate so a capacitor is not (completely at least) uncharged. $\endgroup$ – FourierFlux Nov 15 '17 at 5:47
  • $\begingroup$ I'm not saying it's uncharged. It's just acting like a normal capacitor. And if the net charge is zero as much charge has entered one terminal as has left the other. That is to say, KCL is not violated. $\endgroup$ – Chris Nov 15 '17 at 6:04
  • $\begingroup$ The netcharge isn't zero though given that the charges aren't uniformly distributed - maybe it's approximate. $\endgroup$ – FourierFlux Nov 15 '17 at 22:35
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For a capacitor with one terminal left floating it is possible to insert charge into the other terminal without producing a charge leaving the floating terminal.

If you thought that you pushed charge into one terminal of the "floating" capacitor without any charge exiting the other terminal, then your model neglected some parasitic capacitance between the other terminal and some other structure (like the earth, or the benchtop, or whatever). Once you have included that parasitic capacitance in your model, you'll find that in fact current is flowing out the other terminal and into that other, parasitic, capacitor.

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