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Kirchhoff's Current Law states that the net current through a node is always 0. AFAIK this derives from conservation of charge principle. My question is, is KCL applicable to any electrical component? For example is it applicable to transistors, integrated circuits, etc.

My thought is that it should be applicable, because otherwise, the component would be accumulating charge over time, which I presume is not a stable or desirable (in general) condition. Another possibility would be that the component would be "leaking charge". For example, the component would be "throwing charge into air" etc. In this case, the component is not accumulating charge but charge is being moved out of the circuit. I guess this doesn't happen in general as well.

So my question is, is Kirchhoff's Current Law is applicable to any circuit element? For example, if I add up the currents through pins of an integrated circuit at a given time by taking current directions into account, will I get 0 amperes? Similarly for any other circuit elements. Are there any cases where the net current is not 0 amperes?

Utku
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    Even in your "leaking" case, the net flow through the node is 0, the leak is just another exit path. Note that this is about current flowing through nodes, not about the components (you have e.g. capacitors where you can stuff charge into and it won't come out for a while) – PlasmaHH Jan 15 '16 at 12:18
  • Leaking to the air happens all of the time in a sense: Heat – David Hoelzer Jan 16 '16 at 14:03

3 Answers3

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You are exactly right: due to the conservation of charge, which is a direct consequence of the gauge symmetry of electrodynamics and therefore an unbreakable (according to all current knowledge) law of nature, the sum of current over all possible paths summed over all time is always exactly zero. In the case where the current doesn't go through discrete conductors, it's known as Gauss's Law.

For real life electronic components, Kirchoff's current law is exact to the accuracy that all the current flows through the devices pins. This is usually a very good approximation, since any imbalance in charge tends to get balanced due to electric attraction. Some components though, such as an electron gun, break this on purpose, and therefore from a circuit perspective explicitly break Kirchoff's law. Of course if you account for the stream of electrons coming out, the current law holds again.

Now there's a small but important caveat here: the charge only has to be conserved in the end, not at each moment of time separately. That means that if there's a component that stores net charge, the current can enter there, wait for some amount of time as a charge, and the exit only later. However, no practical component stores appreciable net charge for any appreciable amount of time. This is also true of capacitors and batteries: a capacitor stores an equal amount of positive and negative charge on its plates, whereas a battery has positively charged and negatively charged ions which flow (as electric current) to meet each other when the circuit is in operation. In both cases, the net charge is zero at all times, and so the total charge is constant, and Kirchoff's current law still holds. The same also holds for Flash memories, that is, the charge stored is balanced by a hole in the semiconductor.

However, as the The Photon points out in his answer, for components such as antennas, there may be a small but finite time delay between the current entering a component and exiting it.

Nonetheless, for all practical electronics purposes, for example a complicated IC as specifically mentioned by the OP, Kirchoff's current law holds exactly.

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Timo
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  • So when I measure the net current through the pins of an integrated circuit (or any other type of component) at a given time, I should get net 0 amperes right? – Utku Jan 15 '16 at 12:24
  • @Utku For all practical purposes, barring exceptions such as the electron gun, yes. – Timo Jan 15 '16 at 12:31
  • I'd like to add that there is _one_ important exception: The sum of all currents into a point equal the change in stored charge at that point – Brog Jan 15 '16 at 12:43
  • @Brog You're of course right. I added an explanation concerning that point to my answer. – Timo Jan 15 '16 at 20:21
  • Don't floating-gate transistors (used in flash memory) store very small amounts of charge for a long period of time? – user253751 Jan 16 '16 at 00:58
  • @immibis good point, they do that. As apparently do other types of Flash memories. I couldn't find how much the charge is though in a quick google search, although it must be very little. – Timo Jan 16 '16 at 11:12
  • @iimibis: My understanding is that each transistor used in flash memory, taken as a whole, does not store charge. The excess electrons trapped on the floating gate are balanced by electrons lost by the material on the other side of the thin oxide layer surrounding the floating gate. It doesn't violate Kirchoff's law any more than any other capacitor. – davidcary Jan 16 '16 at 14:11
  • @Timo: The "FG Limitation: Number of Electrons" chart in Chris Buckel's post [Understanding Flash: Fabrication, Shrinkage and the Next Big Thing](http://flashdba.com/2015/02/17/understanding-flash-fabrication-shrinkage-and-the-next-big-thing/) (apparently from page 4 of [Sung Wook Park's presentation](http://regmedia.co.uk/2012/10/11/park_nand_trap_presentation.pdf) ) seems to be saying that early Flash transistors store about 1000 electrons per "programmed" flash transistor, dropping rapidly with each generation. Single-electron flash memory seems to be the minimum theoretically possible. – davidcary Jan 16 '16 at 14:35
  • @davidcary Okay, so assuming the electrons actually do get trapped, if you program every bit in a 4Gb flash in a second, you end up breaking Kirchoff's law by an average of [0.7 \$\mu\$A](http://www.wolframalpha.com/input/?i=2^32+*+%281000+*+electron+charge%29) during that one second. Which I suppose would be measurable with some care, if you could actually program the flash that fast. – Timo Jan 16 '16 at 15:04
  • @Timo: Huh? I agree that 0.7 uA "in" one pin of a flash chip is (with difficulty) measurable with current technology, but I would be very surprised if Kirchoff's law was broken -- i.e., if there wasn't a balancing 0.7 uA flowing "out" some other pin of the flash chip. The charged "trapped" on one plate of a capacitor doesn't violate Kirchoff's law, right? – davidcary Jan 16 '16 at 20:04
  • @davidcary that's the "assuming the electrons actually get trapped" part. Since I'm not an expert in the condensed matter theory of semiconductors, I'm not sure if I'm convinced one way or another whether the electrons stored in the transistor are half of an electron-hole pair from the substrate, leaving zero net charge, or if electrons from the external current actually get trapped there, leaving a non-zero net charge. Do you have a source backing up your understanding, that there's no net charge? – Timo Jan 17 '16 at 13:02
  • @Timo: I'm not a condensed-matter physicist. Please post your question as an independent top-level question. Lots of sources say "The net charge of the capacitor as a whole remains equal to zero." [a](http://www.physics.sjsu.edu/becker/physics51/capacitors.htm) [b](http://amasci.com/emotor/stmiscon.html#six). Some sources that say the gate and the thin oxide acts "like" one plate and the inner insulator of a capacitor. *Exactly* like a capacitor, so there is zero net charge for the entire transistor as a whole (but non-zero net charge on the floating gate alone)? I guess so, but I don't know. – davidcary Jan 17 '16 at 18:27
  • @davidcary For a capacitor, the net charge is indeed zero, that's for sure. The only question is whether the transistors in a Flash device are capacitors in that sense or not. I might actually go ahead and post the question, if I find the time :) – Timo Jan 17 '16 at 18:32
  • @davidcary I asked about the Flash, and got a good answer: http://electronics.stackexchange.com/a/212845/54822 – Timo Jan 23 '16 at 11:58
  • Wow, that question you posted inspired a pretty awesome answer. Thank you. – davidcary Feb 03 '16 at 17:32
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Kirchoff's circuit laws apply to circuits of lumped elements.

If your circuit contains distributed elements, such as transmission lines and antennas, you can't count on KCL applying absolutely.

For example, in a transient analysis current may flow into an antenna momentarily, without flowing out to any other circuit node, at least until 1/2 a cycle later. If we were to do a full electromagnetic analysis of the situation, we could presumably identify a displacement current from the antenna to the surrounding ground and other circuit elements, but usually such an analysis is too complicated to be tractable.

The Photon
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Kirchoffs laws assume that we can divide our circuit into "components" where all charge enters and exits components through a pin and that components have no net charge.

This is only an approximation of reality. All real-world components have capacitance to each other and the universe in general. When voltages change this stray capacitance must be charged or discharged which means a net transfer of charge between components. When components physically move the capacitance between them changes and a net charge movement is needed to keep the voltages the same.

Will that affect be measurable? that very much depends on the speeds at which your circuit works and the size of your components.

Peter Green
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