[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.