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Now let's talk about admittance and
how to use it in current dividers.

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Remember that resistance is
a value that's given in ohms.

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It's inverse,
1 over R is called admittance.

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We usually use G to represent that and
it's given in inverse ohms or

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ohms to the -1, or 1 over ohms,
and sometimes we call that Mhos.

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Kinda see it's ohms backwards.

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So admittance,
right here is one over the resistance.

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We use that in a lot of good math.

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For example, remember that if we have
resistors in series, R1, R2, and

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R3, that if we want to
have the total resistance

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over this region, R = R1 + R2 + R3.

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If we had values that were in parallel,
then we had to handle that differently.

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One very easy way of handling that
is to put admittances in parallel.

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If we use values G1, G2,
and G3, then we can say

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that the entire admittance G,
from this point a to this point b,

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so G from a to b = G1 + G2 + G3.

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So it's very handy to add up resistors in
parallel by treating them as admittances

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instead of as resistors.

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Now let's do a current
divider using resistance.

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Remember that when we've got
a current divider like this,

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we first have to combine two
of the resistors in parallel.

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Let's say that what I want to find is I1,
so I would combine these in parallel.

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This would be equal to R2
times R3 over R2 + R3.

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Then if I wanted to find I1,

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that would be equal to I0 times
the resistors that it's not going through.

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Which is this R2 times R3 over R2 + R3

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divided by all the resistors,

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which is R1 + R2R3 over R2 + R3.

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That's how we handle a current
divider using resistance.

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But if we wanted to use
admittance instead,

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here's the way that we can do that.

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We don't even need to combine
this into series and parallel,

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we're just going to be able to say
that I1 = Io times the admittance

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that it is going through,
divided by G1 + G2 + G3.

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That's really a lot easier than what
we did on the previous page, so

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I'm gonna say this is a really cool
way of doing current dividers.

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I'm going to show you how similar
that is to doing voltage dividers.

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If we have, so this is a voltage divider,
if we have resistors in series,

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R1, R2, and R3,
let's say that I wanted to find V1.

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Then V1 would be equal to,
this is the total voltage across here,

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V0 times R1, divided by R1 + R2 + R3.

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You can see the form of these two
equations is equivalent except,

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that one is handling parallel admittances,
the other is handling series resistances.

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Now let's do an example just with numbers,
let's do a resistive current divider

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like this with 1 ohm, a 2 ohm,
and a 3 ohm resistor.

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And let's say that I want to find
I1 given that I have 10 amps

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of current going in, that is I0.

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So we will first of all need to
convert this two admittances and

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what we would have Is 1 divided by 3 mhos,

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1 divided by 2 mhos and
1 divided by 1 mhos.

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And again, we're looking for
I1 with an I0 of 10 amps going in.

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So what we would say is, I1 = 10 amps,

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that's the I0 value times the admittance
that it is going through,

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1 mho, divided by the sum of
all of the other admittances.

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And that's our I1 value.

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That's really very simple, whole lot
simpler than doing it with resistances.