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Let's see if we can apply
what we've learned to a

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particularly hairy problem
that I have constructed.

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So let me see how I can
construct this.

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So let's say in parallel, I have
this resistor up here.

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And I try to make it
so the numbers work

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out reasonably neat.

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That is 4 ohms. Then I have
another resistor right here.

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That is 8 ohms. Then I have
another resistor right here.

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That is 16 ohms. And then, I
have another resistor here,

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that's ohms. Actually, I'm now
making it up on the fly.

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I think the numbers
might work out OK.

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16 ohms.

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And let's say that now here in
series, I have a resistor that

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is 1 ohm, and then in parallel
to this whole thing-- now you

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can see how hairy it's getting--
I have a resistor

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that is 3 ohms. And let's say
I have a resistor here.

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Let's just make it
simple: 1 ohm.

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And just to make the numbers
reasonably easy-- I am doing

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this on the fly now-- that's
the positive terminal,

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negative terminal.

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Let's say that the voltage
difference is 20 volts.

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So what I want us to do is,
figure out what is the current

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flowing through the wire
at that point?

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Obviously, that's going to be
different than the current at

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that point, that point, that
point, that point, all of

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these different points, but it's
going to be the same as

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the current flowing
at this point.

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So what is I?

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So the easiest way to do this
is try to figure out the

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equivalent resistance.

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Because once we know the
equivalent resistance of this

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big hairball, then we can just
use Ohm's law and be done.

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So first of all, let's just
start at, I could argue, the

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simplest part.

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Let's see if we could figure out
the equivalent resistance

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of these four resistors
in parallel.

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Well, we know that that
resistance is going to be

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equal to 1/4 plus 1/8
plus 1/16 plus 1/16.

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So that resistance-- and
now it's just adding

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fractions-- over 16.

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1/4 is 4/16 plus 2/16 plus 1
plus 1, so 1/R is equal to 4

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plus 2 is equal to 8/16-- the
numbers are working out-- is

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equal to 1/2, so that equivalent
resistance is 2.

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So that, quickly, we just
said, well, all of these

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resistors combined is equal to
2 ohms. So let me erase that

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and simplify our drawing.

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Simplify it.

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So that whole thing could now
be simplified as 2 ohms. I

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lost some wire here.

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I want to make sure that
circuit can still flow.

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So that easily, I turned that
big, hairy mess into something

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that is a lot less hairy.

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Well, what is the equivalent
resistance of this resistor

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and this resistor?

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Well, they're in series, and
series resistors, they just

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add up together, right?

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So the combined resistance of
this 2-ohm resistor and this

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1-ohm resistor is just
a 3-ohm resistor.

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So let's erase and simplify.

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So then we get that combined
resistor, right?

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We had the 2-ohm that we
had simplified and

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then we had a 1-ohm.

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So we had a 2-ohm and a 1-ohm
in series, so those simplify

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to 3 ohms.

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Well, now this is getting
really simple.

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So what do these two resistors
simplify to?

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Well, 1 over their combined
resistance is

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equal to 1/3 plus 1/3.

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It equals what?

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2/3.

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1/R is equal to 2/3, so R is
equal to 3/2, or we could say

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1.5, right?

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So let's erase that and
simplify our drawing.

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So this whole mess, the 3-ohm
resistor in parallel with the

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other 3-ohm resistor is equal
to one resistor with a 1.5

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resistance.

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And actually, this is actually
a good point to give you a

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little intuition, right?

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Because even though these are
3-ohm resistors, we have two

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of them, so you're kind of
increasing the pipe that the

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electrons can go in by a
factor of two, right?

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So it's actually decreasing
the resistance.

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It's giving more avenues for the
electrons to go through.

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Actually, they're going to be
going in that direction.

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And that's why the combined
resistance of both of these in

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parallel is actually half
of either one of these

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resistances.

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I encourage you to think about
that some more to give you

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some intuition of what's
actually going on with the

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electrons, although I'll do a
whole video on resistivity.

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OK so we said those two
resistors combined-- I want to

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delete all of that.

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Those two resistors combined
equal to a 1.5-ohm resistor.

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That's 1.5 ohms. And now all
we're left with is two

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resistors in parallel, so the
whole circuit becomes this,

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which is the very basic one.

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This is a resistor: 1.5
ohms, 1 ohm in series.

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Did I say parallel just now?

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No, they're in series.

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1.5 plus 1, that's 2.5 ohms.
The voltage is 20

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volts across them.

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So what is the current?

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Ohm's law.

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V is equal to IR.

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Voltage is 20 is equal to
current times our equivalent

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resistance times 2.5 ohms. Or
another way to write 2.5 five

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is 5/2, right?

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So 20 is equal to I times 5/2.

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Or I is equal to 2/5 times
20, and what is that?

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2/5 is equal to I
is equal to 8.

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8 amperes.

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That was not so bad,
I don't think.

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Although when you saw it
initially, it probably looked

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extremely intimidating.

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Anyway, if you understood that,
you can actually solve

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fairly complicated circuit
problems. I will see you in

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future videos.