# Kirchhoff’s current law | Circuit analysis | Electrical engineering | Khan Academy

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– [Voiceover] Up to now we’ve talked about resistors and capacitors

and other components, and we’ve connected them up and learned about Ohm’s

law, for resistors, and we’ve also learned some

things about series resistors, like we show here. The idea of Kirchhoff’s Laws, these are basically common sense laws that we can derive from

looking at simple circuits, and in this video we’re gonna work out Kirchhoff’s Current Law. Let’s take a look at these

series resistors here. There’s a connection point right there, and that’s called a node, a junction. And one of the things we know is that when we put current through this, let’s say we put a current through here. And we know that current

is flowing charge, so we know that the charge

does not collect anywhere. So that means it comes

out of this resistor and flows into the node, and that goes across and

it comes out on this side, all the current that comes in comes out. That’s something we know, that’s the conservation of charge, and we know that the charge

does not pile up anywhere. We’ll call this current i1. And we’ll call this current i2. And we know, we can just write

right away, i1 equals i2. That seems pretty clear from

our argument about charge. Now let me add something else here, we’ll add another resistor to our node. Like that. And this now, there’s gonna be

some current going this way. Let’s call that i3. And now this doesn’t work anymore, this i1 and i2 are not

necessarily the same. But what we do know is

any current that goes in has to come out of this node. So we can say that i1 equals i2 plus i3. That seems pretty reasonable. And in general, what we have here isn’t, if we take all the current flowing in, it equals all the current flowing out. And that’s Kirchhoff’s Current Law. That’s a one way to say it, in mathematical notation,

we would say i in, the summation of currents going in, this is the summation sign, is the summation of i out. That’s one expression of

Kirchhoff’s Current Law. So now I want to generalize

this a little bit. Let’s say we have a node, and we have some wires going into it, here’s some wires connecting up to a node. And there’s current going into each one. I’m gonna define the current arrows, this looks a little odd,

but it’s okay to do. All going in. And what Kirchhoff’s Current Law says is that the sum of the currents going into that node has to be equal to zero. Let’s work out how that works. Let’s say this is one

amp, and this is one amp, and this is one amp. And the question is, what is this one? What’s that current there? If I use my Kirchhoff’s

Current Law, express this way, it says that one plus one plus one plus i, whatever this i

here, has to equal zero. And what that says is

that i equals minus three. So that says, minus three amps flowing in is the same exact thing as

plus three amps flowing out. So one amp, one amp, one amp comes in, three amperes flows out. Another way we could do it, equally valid, this is just three ways to

say exactly the same thing. I have a bunch of wires going

to a junction, like this. And this time I define

the currents going out, let’s say I define them all going out. And this same thing works. The sum of the currents, this time going out, I’ll go back over here, I’ll write in, all the currents going in. That has to equal zero as well. And you can do the same exercise, if I make all these one amp, and ask, what is this

one here, what is i here, outgoing current, it’s one plus one plus one plus one, those are the four that I know, and those are the ones going out, so what’s the last one going

out, it has to equal zero. The last one has to be

minus four equals zero. So this is a current

of minus four amperes. So that’s the idea of

Kirchhoff’s Current Law. It’s basically, we’ve reasoned through

it from first principles, because everything that comes in has to leave by some route, and when we’ve talked about it that way, we ended up with this expression for Kirchhoff’s Current Law. And we can come up with a slightly smaller mathematical expression, if we say, let’s define all the

currents to be pointing in. Some of them may turn out to be negative, but then that’s another way to write Kirchhoff’s Current Law. And in the same way, if we define all the currents going out, and you actually have

your choice of any of these three any time

you want to use these. If we define them all going out. This is Kirchhoff’s Current Law, and we’ll use this all the time

when we do circuit analysis.

wild killerPost authorfirst

Jimmy D29Post authorlol 1 day too late, had test td… haha

kishan chauhanPost authorhey , love your videos

kishan chauhanPost authorcan I download them from somewhere please? š

bigworld 12Post authorjust remember guys that current represents the NUMBER of electrons

TaylorPost authorNOW YOU COME OUT WITH THIS???? MY FINAL WAS A WEEK AGO! jk ily

Aoishika SrivastavaPost authorkhan academy's biology explanation is better than physics' explanation

JavaPost authorCan we say that every electron entering the circuit, will not disapear in a blackhole somewhere in the middle, and will come back on the OUT side ?

syahmianasssPost authorsalman khan

Bibek Raj DhungelPost authoris it possible to have negative input current?

how can we provide the negative current?

Chelsea BentonPost authorThis guy sounds so much like bill Murray or bill Paxton that it's distracting

Luis PintoPost authorhow is the current the same, wouldnt the resistors convert the electricity into heat?

Shahidh IlhanPost authorwhat is the difference between +3A and -3A?

JayMPost authorAwesome video!!! Saved me on my test!!!

per sonaPost authorthank you

caleb leePost authoromg bloody khan just change the arrows to a different direction dont put -ve u complicate me

Iqra ZulfiqarPost authorcan u tell me how we plot 5 ampear AC and 5 amp DC graph

JasPost authorSo amps can be negative numbers??

zPR0-PubGPost authorsone topics in your videos are missing like..

wheatstone bridge ..

biot savarts law.. nd some more

NixTrix MusicPost authori got 92% in my physics test thanks=A

Jhen Dela RosaPost authorLazy instructor…..no specific example

Miles Emanuel PaavolaPost authorThank you for sharing! š Your videos are always great.

Hyjda DynasurPost authorWheatstone bridge

Blaze OfficialPost authoramazing one.. respect for you

Pengembara SamuderaPost authormake a video about wheatstone bridge please

amiestudycirclePost authorVery informative lecture. Kudos.

Uchiha MadaraPost authorHave a midterm in 2 hours. Of course khan academy has a video on this lol

Jules BartowPost authorThis is way too complicated. My momma taught me the simple way: Gzintas = Gzoutas. Translation: What Goes Into must Go Out Of.

kewpie capiePost authori got 99% boards in science thanks

h yPost authorGreat understanding

Rudra JhaPost authorI love Sal Khan .

He is like a God to me

abdullaa tahaPost authorWhat if half of the wires are in and the half are out?

sami kechichePost authorThank you so much your videos helped me so much to better understand physics better than my own teachers Iām from Tunisia and it s in a mess right now so thank you very much I m very grateful!!!š

Rik DeBaccoPost authorThis made literally zero sense(except for the ohms law part). Thanks for trying tho.

open circuitPost authorit is not enough

Brad CozinePost authorIf that's Kirchhoff's Current Law, what was Kirchhoff's Old Law?

Jacob van DijkPost authorKIRCHHOFF: the english word "church" is related to the german word "kirche"; the german word "hof" can be translated by the word "yard"; in the old days grounds around churches were used to bury people; so, a good translation of "kirchhoff" is "graveyard".

Gustav Robert KirchhoffPost authorNice vid bro!

Chandhini ChowdaryPost authorThank you..it was very helpful š