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When I was first learning about KCL, I learned it as describing the relationship that nodes cannot store charge. But now, I have seen that it can also be applied to the case of circuits with capacitors, yet capacitor plates form nodes that can store charge. So how does KCL make sense in this case?

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Capacitors store a dipolar charge, but not a net unbalanced charge, i.e. one plate holds some net charge \$Q\$ and the other plate holds a net charge of \$-Q\$, while the overall net charge over the entire capacitor is zero.

Putting a current into the capacitor doesn't contradict KCL in any way - for example, if you put a current of +1 Ampere into the electrode connected to one plate, that plate's net charge increases by one coulomb per second. At the same time, the other plate's net charge decreases by one coulomb per second, meaning that a current of 1 ampere is flowing out of that second plate. Of course, an electric field, and hence a voltage, builds up across the plates in the process.

Charge has thus been conserved with no contradiction.

If you wish to go further and investigate the continuity of current through the dielectric between the plates, then you need to include displacement current in your accounting. However, for a simple lumped circuit where the capacitor and its plates/E-fields are internal to the lumped element, there's no need to do so.

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