00:03
Okay, so let's take a look at this cool circuit.
00:06
We have two batteries, a bunch of resistors, and our goal is to find the current and voltages for each resistor.
00:14
What i like to do when i see a circuit is i find the biggest battery and make sure i put zero volts at the bottom conductor, where the negative terminal is.
00:25
And everywhere along a conductor, i get zero volts.
00:29
Notice that on the left, i raise a voltage.
00:33
Voltage after the battery by 12 volts and similarly in the middle, then that node will be 20 volts.
00:39
I still have some unknown nodes, so let's label va at that top middle node and vb on the far right node.
00:47
We have to define our current.
00:48
So i'm going to go ahead and call this current one and we'll call this current two and that middle one from the battery current three.
01:01
Okay, so let's go ahead and do kirkov's current law, and we're going to do it at this node, the center node.
01:10
And basically, kirkov's current law tells us that all the currents going in need to equal the currents leaving.
01:19
And we can find each current by holmes law, the voltage over the resistance gives us our current.
01:25
And we'll do it based on the resistor.
01:27
So if i look at r1, the voltage difference is 12 minus.
01:32
B .a over 100.
01:35
I'm going to leave out the units for now because we're going to manipulate this equation, but we'll make sure we have units at the end.
01:42
I3 is 20 minus va over 270 and that equals va over.
01:53
I'm just going to do the total resistance of 200 and 2 oms.
01:56
It's in series, r and 3 and our 4 are in series.
01:59
So we can go ahead.
02:02
And just add those resistances together.
02:06
Okay, i want to solve for va.
02:09
And what i'm going to do is first split up these fractions because i need to isolate va by itself.
02:18
So i'm not going to worry about a common denominator at this point.
02:21
I'm just going to get everything in the right position and then use the calculator.
02:27
Okay, so i'm going to bring all the va terms to the right, leaving on the left 12 over 100 plus 20 over 270 equals va.
02:40
And that will be one over 100 plus 1 over 270 plus 1 over 202 on the right.
02:51
I brought over the two va terms, factored out the va and then we can solve.
02:56
At this point, i'm going to go ahead and use my calculator because i want to value for va on the the left we get 12 over 100 plus 20 over 270 that is 0 .194074 .1.
03:14
That has to equal va times this.
03:17
So 1 over 100 plus 1 over 270 plus 1 over 202 gives me 0 .01865.
03:32
So va then will be what i get when i divide both sides by the .018 term.
03:39
So i will take 0194 -0741 divided by the 0 .01 -8 -6 -542.
03:50
And i get the a, b, oops, i accidentally multiplied, got a really bizarre number.
03:56
Let's divide instead.
03:59
And that gives me 10 .4 volts.
04:07
Okay, so va is 10 .4 volts.
04:10
Now notice we can plug back in our va value into each of these terms here, and that will allow us to get our currents.
04:19
So we'll have our currents right away.
04:21
So let's go do that.
04:23
Okay, so first let's find i -1.
04:25
I1, by the way, is the current going through r1...