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- [Voiceover] Up to now we've talked about

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resistors and capacitors
and other components,

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and we've connected them up

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and learned about Ohm's
law, for resistors,

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and we've also learned some
things about series resistors,

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like we show here.

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The idea of Kirchhoff's Laws,

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these are basically common sense laws

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that we can derive from
looking at simple circuits,

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and in this video we're gonna

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work out Kirchhoff's Current Law.

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Let's take a look at these
series resistors here.

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There's a connection point right there,

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and that's called a node, a junction.

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And one of the things we know is that

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when we put current through this,

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let's say we put a current through here.

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And we know that current
is flowing charge,

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so we know that the charge
does not collect anywhere.

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So that means it comes
out of this resistor

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and flows into the node,

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and that goes across and
it comes out on this side,

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all the current that comes in comes out.

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That's something we know,

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that's the conservation of charge,

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and we know that the charge
does not pile up anywhere.

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We'll call this current i1.

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And we'll call this current i2.

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And we know, we can just write
right away, i1 equals i2.

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That seems pretty clear from
our argument about charge.

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Now let me add something else here,

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we'll add another resistor to our node.

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Like that.

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And this now, there's gonna be
some current going this way.

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Let's call that i3.

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And now this doesn't work anymore,

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this i1 and i2 are not
necessarily the same.

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But what we do know is
any current that goes in

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has to come out of this node.

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So we can say that i1 equals i2 plus i3.

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That seems pretty reasonable.

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And in general, what we have here isn't,

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if we take all the current flowing in,

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it equals all the current flowing out.

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And that's Kirchhoff's Current Law.

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That's a one way to say it,

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in mathematical notation,
we would say i in,

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the summation of currents going in,

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this is the summation sign,

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is the summation of i out.

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That's one expression of
Kirchhoff's Current Law.

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So now I want to generalize
this a little bit.

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Let's say we have a node,

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and we have some wires going into it,

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here's some wires connecting up to a node.

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And there's current going into each one.

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I'm gonna define the current arrows,

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this looks a little odd,
but it's okay to do.

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All going in.

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And what Kirchhoff's Current Law says

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is that the sum of the currents

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going into that node

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has to be equal to zero.

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Let's work out how that works.

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Let's say this is one
amp, and this is one amp,

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and this is one amp.

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And the question is, what is this one?

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What's that current there?

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If I use my Kirchhoff's
Current Law, express this way,

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it says that one plus one plus one

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plus i, whatever this i
here, has to equal zero.

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And what that says is
that i equals minus three.

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So that says, minus three amps flowing in

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is the same exact thing as
plus three amps flowing out.

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So one amp, one amp, one amp comes in,

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three amperes flows out.

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Another way we could do it, equally valid,

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this is just three ways to
say exactly the same thing.

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I have a bunch of wires going
to a junction, like this.

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And this time I define
the currents going out,

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let's say I define them all going out.

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And this same thing works.

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The sum of the currents,

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this time going out,

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I'll go back over here, I'll write in,

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all the currents going in.

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That has to equal zero as well.

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And you can do the same exercise,

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if I make all these one amp,

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and ask, what is this
one here, what is i here,

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outgoing current,

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it's one plus one plus one plus one,

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those are the four that I know,

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and those are the ones going out,

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so what's the last one going
out, it has to equal zero.

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The last one has to be
minus four equals zero.

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So this is a current
of minus four amperes.

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So that's the idea of
Kirchhoff's Current Law.

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It's basically,

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we've reasoned through
it from first principles,

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because everything that comes in

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has to leave by some route,

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and when we've talked about it that way,

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we ended up with this expression

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for Kirchhoff's Current Law.

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And we can come up with a slightly smaller

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mathematical expression, if we say,

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let's define all the
currents to be pointing in.

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Some of them may turn out to be negative,

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but then that's another way

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to write Kirchhoff's Current Law.

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And in the same way,

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if we define all the currents going out,

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and you actually have
your choice of any of

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these three any time
you want to use these.

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If we define them all going out.

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This is Kirchhoff's Current Law,

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and we'll use this all the time
when we do circuit analysis.