00:01
This is an example showing how to simplify a circuit down into a single resistor in series with a battery.
00:10
So we'll start off with a battery voltage v.
00:15
And let's just put some resistors in.
00:19
Here's the first resistor.
00:22
And then two more resistors, r2, r3.
00:27
And what you want to do is figure out whether resistors are in series or parallel and come up with what's called an equivalent resistance for that system.
00:45
So definition of parallel means the same voltage across them.
00:50
And that means that the resistors in parallel must share the same top and bottom, kind of like they're going down a hill.
01:00
Different directions, but the hill has a common top and a common bottom.
01:06
So r2 and r3 are in parallel.
01:09
And so we're going to replace that with a parallel resistance.
01:15
And the formula for parallel resistance is to take the inverses of the two resistances or however many there are, and then take the inverse of that.
01:29
And we could do some simplification of this using a little bit of algebra.
01:39
We can find a common denominator in that inverted fraction, and then it's a little bit easier to invert.
01:49
And i'll be doing that.
01:50
I'll be using some algebra to get my expressions in a more simple form.
01:59
Then what's true is we can replace those two resistors, r2 and r3, with their parallel equivalent, and then that parallel equivalent is in series with r1.
02:12
And that's a fairly simple expression.
02:16
The r series is just r1 plus whatever is in series with it.
02:23
There could be multiple resistors in series.
02:28
So we'll, again, find a common denominator in order to add the first.
02:39
Fraction in the parallel to the r1.
02:46
And then you kind of have a funny looking total resistance, r1, r2 plus r1, r3 plus r2, r2, r3 over r2 plus r3.
03:08
And ordinarily you wouldn't have to write out such a large fraction if you had numbers for the resistances.
03:18
It would be a fairly easy thing...