00:01
In this problem, you have a circuit, and your goal is using kirchhoff's rules to get the three currents, i -1, i -2, and i -3.
00:14
Now, before i get into anything, any of the rules, understand one thing.
00:19
They've given you all these current directions and the later traversed the loops.
00:26
It's totally your choice.
00:29
You make assumptions.
00:31
You can draw your arrows for i -1 and i -2 and i -3, any which way you want.
00:35
You can traverse your loops any which way clockwise, counterclockwise, doesn't matter.
00:42
You choose it.
00:43
Just as long as you are consistent with your assumptions about your currents, you're fine.
00:51
You can do whatever.
00:52
You can set your own assumptions.
00:56
If you find that a current, when you do that, when you do the full analysis, ends up negative.
01:03
That meant that you may have assumed, say, you assumed that i want is going to the right, but in reality, if it turned out to be negative, it's moving to the left.
01:15
So that tells you that your assumption is the opposite of what it is.
01:20
But you're free.
01:21
So don't feel that you, there is one certain way to traverse a loop or one way currents, somehow you've got to know the direction of the currents already.
01:31
The whole purpose of these rules are to find that information out.
01:38
Okay.
01:39
Now, kerchow's rules got two, one for currents, going into a branch, point one for voltage changes drops and increases as you go around a loop so let's look at a is a branching point currents come in and one goes out it's a branching point so they kind of one two you think form three maybe maybe it's other way around maybe we'll have to see to see maybe two breaks up into one and three don't know we'll find out at a.
02:19
We got i1, i2 coming in.
02:22
So i1 plus i2 is equal to i3.
02:26
I call it equation 1.
02:29
So that's for current.
02:33
Now we're going to use a loop rule.
02:36
This deals with the voltage increases and decreases to go around the loop.
02:39
It's like a water wheel.
02:42
The wheel takes a bit of water, brings it up, gives it potential energy, and then as that water comes down, it loses all the potential energy.
02:49
Same thing here.
02:50
You start to charge, starts here, positive charge, starts here, it gains some voltage, but then when it goes through this resistor, it's going to lose and lose, and it's going to end up losing everything it was given, just like the water and a water wheel would as it got back to the ground where it was picked up initially.
03:08
Same exact idea.
03:11
Same exact idea.
03:14
Okay, so loop one, and we're going to do clockwise, well, we're following their arrows, clockwise traversal.
03:22
Like i said, you don't have to.
03:25
You know, you can practice, convince yourself that if you were to go around the other way, if you would go around this way, counterclockwise.
03:34
And you could leave this one alone.
03:36
In the end, you'd get the same answers.
03:40
Okay.
03:41
So, let me give my, you can see it.
03:43
So let's start here at the negative plate of the battery.
03:47
So you're going to go up v1 volts.
03:51
First i'm writing in symbols, then we'll put in our numbers.
03:54
And then now currents flow to lower potential.
03:58
So you're dropping.
04:00
You're dropping.
04:00
You're dropping.
04:00
You're being in potential from the left to the right and that's given by oms law ir minus i1 r1 and the same thing through three minus i3 r3 is equal to zero that zero represents the fact that whatever was put in whatever deposit was made into like a bank account you had two withdrawals and with a loop you're basically giving the rules is whatever you do during that day all your addition, subtractions, your deposit, your withdrawals, in the end, it's got to come back the way it started.
04:39
That's the analogy you could use, if you like.
04:43
We can put in some numbers here because we're going to end up with a simultaneous equation.
04:49
10 minus 10 i1 minus 40, i3, that's equal to zero.
04:56
Divide all terms by 10, you get one minus i1, minus 4, i3, is equal to zero, i'll call the equation two.
05:07
Okay, so that was loop one.
05:09
Loop two, we're gonna do counterclockwise.
05:16
Traversal...
