00:01
There are two rules for circuits that can be used to analyze almost any circuit with a little bit more rules about the components in the circuit.
00:12
And these are known as kirchhoff's rules.
00:17
So we see the name kirchhoff associated with these.
00:25
And they are really nothing more than conservation of charge and conservation of energy.
00:31
So conservation of charge says that you can't lose charge in the circuit.
00:38
Where that becomes important is at what is called a junction, a place where a current may split and become two currents.
00:50
So i have identified the two junctions that would occur in the circuit shown.
00:57
And we really need to be looking at currents flowing in versus flowing out of those junctions.
01:04
But basically what flows in must flow out.
01:08
So it's usually good idea to start off and define currents in each of the branches of the circuit.
01:16
And i am going to pick i -1 coming out of the top battery.
01:24
Usually currents flow out of positive terminals.
01:27
And i -3 i'm going to show coming out of the positive terminal of the bottom battery.
01:34
And it will flow around.
01:36
And notice that those are two currents going into the same place.
01:41
If that was traffic, they couldn't just jam up that place without exploding at some point.
01:48
So the idea is they combine together to form a third current, which we'll call a i2, because it goes through resistance too.
01:58
And the kirchhoff's rule says that the sum of the currents into a junction has to equal the sum coming out.
02:12
With the simple situation we have shown, we have i3 and i1 going in, and we've got i2 flowing out.
02:22
So our junction equation would be this.
02:26
If you're trying to solve for the currents, that isn't enough equations, of course.
02:32
We see there are three currents, and we're going to need three equations.
02:36
So the second set of rules is conservation of energy, and it involves a loop.
02:50
What do we mean by a loop? a loop is nothing more than a full circuit that starts in one place and goes all the way around, comes back to the same place, just as the name suggests.
03:03
There are actually three loops in the circuit.
03:05
We are just going to need two of them to get the three equations.
03:09
So i am going to call loop one, kind of the top loop that loops through e1, r1, and r2.
03:18
So loop one, give that a different symbol.
03:24
So loop 1 goes through e1.
03:37
R1, r2, and then back to its starting place.
03:42
And what is true is that the sum of the voltage gains going around the loop has to equal the sum of voltage drops.
03:53
And we'll take a look at that first loop to see what that means.
03:57
But just like you had to pick a loop, you have to pick a starting place.
04:02
And i'll start, i usually like to start on negative terminal of a battery.
04:06
And if i walk in the direction of i -1 flow, i first run into the battery and i get a 9 -volt boost.
04:21
If i go in the direction of current flow across the resistor, i'm dropping.
04:27
So that would be 28 times i -1 for a drop.
04:32
And then if i continue to go through the resistance to notice that i'm going in the direction of current flow in that resistor 2, but in the amount of 66 times i2.
04:51
And if we'll call loop 2 the bottom, a loop, so i'll have to roam a numeral a little funny, so it doesn't look like a current.
05:04
But the same sort of analysis, i'll start on the negative terminal of the battery and walk in the direction of i3.
05:12
And if you get the current flowing incorrectly, it will show up as a negative answer.
05:18
So you don't have to worry too much, but i usually choose a certain convention.
05:25
So we first come to a 12 -volt boost from the battery, and then we get a drop in the amount of minus.
05:35
It's on the negative side, so we don't need the minus...