- [Voiceover] In the last video,
we introduced the idea of parallel resistors.
These two resistors are in parallel with each other
because they share nodes and they have
the same voltage across them.
So that configuration is called the parallel resistor.
And we also showed that these two resistors
could be replaced by a single resistor
we labeled this one R1, this is R2.
We showed that we can replace R1 and R2
by an equivalent parallel resistor
with this expression here for two resistors.
RP ..one over RP equals one over R1 plus
one over R2.
So that's how you calculate the equivalent resistance
for two parallel resistors.
Now you can ask and it's a good thing to ask
what if there's more resistors?
What if there's more resistors in parallel here?
What if I have R3 and R4 and RN
all connected up here.
What happens in this expression?
So like we did before we had a current here
and we know that current comes back here.
The first current split, some current goes
down through R1, some current goes through R2
and if we had more resistors some goes down through
R3, and some goes through RN.
So the current basically is coming down here
and splitting amongst all the resistors.
Now all the resistors share the same
all the resistors share the same voltage.
So that's just V, let's label V.
That's just V, they all share the same V
and they all have a different current.
Assuming they all have a different resistance value.
So we do exactly the same analysis
that we did before.
Which was, we know that I here
here
has to be the sum,
there's the summation symbol
of all the I's.
I1, plus I2, plus I3
plus IN, that's as many as we have.
So we know that's true.
And we also know that
the current, we also know that the current
in each individual resistor
IN
is equal to one over that resistor
times V, and V is the same for every one of them.
So now we substitute this equation into here for I
For I.
We get the big I, the overall I is equal to
voltage times, it's gotta be a big expression,
one over R1 plus one over R2
plus one over R3, plus as many resistors as we have
One over RN, like that.
And we do the same thing as we did before
which was we say that this expression here
is equivalent to one parallel resistor
we're going to make the equal to one parallel resistor.
So this whole guy here is gonna become
one over RP
That gives us a way to simplify any number of resistors
down to a single parallel resistor
and I'll write that over here.
So for N resistors, multiple resistors
one over RP the equivalent parallel resistor
is equal to the same thing.
One over R1 plus one over R2
plus dot, dot, dot, one over RN.
So this tells you how to simplify
any number of parallel resistors
down to one equivalent parallel resistor.