[BLANK_AUDIO].
In this example, we have a network of several resistors.
And some of them are already in the configurations that are easy for us to
analyse, but other ones are not. For example, if you look over here, where
we have the 7 ohm resistor, the 8 ohm resistor, and the 3 ohm resistor.
They're not directly in any simple configuration.
Well, we don't have to do these right away.
We can do successive implementations of the res-, the parallel resistive circuits
that we've looked at, to work our way over to a solution.
And so this shows us how we can do that in a multi-step process.
So, the first thing we're going to look at is that we have this 7 ohm resistor
here and this 8 ohm resistor here. And these two resistors are in series
because they're not connected to anything else.
But, they are connected to each other by this one simple node.
So I know that the total resistance of this section [SOUND] is just the sum of
their individual resistances. So it's 15 ohms.
Once we've done that, we now notice that this combined resistance is now in
parallel with this 3 ohm resistance. So we can then do a calculation of that.
So we have 1 over 15, plus 1 over 3, to negative 1.
Getting common denominators,
[BLANK_AUDIO]
6 over 15, to the negative 1. Then we can do a little bit of
simplifying to get five halves of an ohm. [BLANK_AUDIO].
So now, we've found an equivalent resistance for all of that section.
But once we know what the resistance is of that section.
You'll notice now that is serious with this 3 half ohm resistor.
So again, we can just sum those together, three halves plus five halves, gives us
eight halves, or 4 ohms. That gives us this section.
This 4 ohm resistor is now in parallel with the 12 ohm resistor.
[BLANK_AUDIO]. So we can simply do that equation.
[BLANK_AUDIO]. It's also interesting to notice that
whenever you're doing parallel resistances, the total resistance will
always be smaller than each of the individual resistances.
So it's a good thing to check your work. [BLANK_AUDIO].
In this case I've got 3 ohms, which is less than 12, and it's less than 4.
So it's probably right. With this 3 ohm resistor, this is now in
series with this 3 ohm resistor and this 2 ohm resistor.
So 3 plus 3 plus 2 is 8 ohms. And now that whole combination.
Then we'll do a nice circle to keep track of where we are.
That is all in parallel with an 8 ohm resistor.
So we can do that, 1 over 8, and 1 over 8.
Whenever you have two resistors that have the same resistance, and you're combining
them in parallel like this, it's always half of the individual resistances.
Because you always end up with having 2 over the individual resistances that you
invert, so it's now going to be half of that 4 ohms.
And at this point, we've just add up the remaining, because now the 7 ohm and the
2 ohm resistor are going to be in serious with that 4 ohm equivalent resistance.
So, 7 plus 4 plus 2
[BLANK_AUDIO]
[SOUND]
is 13 ohms. [SOUND].
So, what we've been able to discover, is that if we go from the top node to the
bottom node that are held open, in this particular example, we can replace the
whole mess. All of these resistors with one single
resistor that is 13 ohms, and we're going to get the same behavior.