00:01
So we have this circuit and we would like to first find the total resistance.
00:04
I'm just going to draw the circuit really quickly.
00:07
So we have this 12 -volt battery and we have one branch of the circuit with a 1 ,000 -oam resistor.
00:21
So this is r1 and it has 1 ,000 oms.
00:27
And then we have another branch where there are three resistors.
00:35
And this is r2, and it has 680 oms.
00:42
This is r3, it has 4 ,700 oms.
00:49
And this is r4, and it has 1 ,500 oms.
00:57
So in order to find total resistance, we are going to have to first get the two branches to be one single resistor each.
01:05
And so we know that here we have this branch, and we know that this branch is a thousand oms.
01:15
But we also have this other branch with three resistors.
01:19
And i'm going to outline that in dots as well.
01:28
And so both dotted off portions are parallel to one another.
01:39
And so, well, first, for the larger dotted off branch, find what the total resistance is in there by adding up those three resistors in series.
01:51
So for this branch right here, the total resistance of this branch, we can call this branch b, and this can be branch a.
02:06
The total resistance in branch b will be r2 plus r3 plus r4, and i guess we can say that this is the resistance in branch b.
02:21
So what we're going to get is that the total resistance in branch b is 680 oms plus 4 ,700 oms plus 1 ,500 oms, plus 1 ,500 oms.
02:38
And we get that the total resistance in branch b is 6 ,880 oms.
02:46
But we want total resistance for the entire circuit.
02:49
So total resistance, we have to add these up in parallel now.
02:57
So we'll have the resistance from branch a, which is only r1, plus one over the resistance from branch b, which we can say is rb.
03:11
So we're just going to plug in numbers, but first we can say that our total, actually, let's not even bother doing that.
03:21
We'll just throw it in our calculator.
03:23
So we'll have 1 over our total is equal to 1 divided by 1 ,000 oms plus 1 divided by 6 ,800 oms.
03:39
And we know that for parallel, the total resistance will always be lower than the lowest resistor in the parallel branches.
03:50
And so we can expect our total resistance to be under 1 ,000.
03:55
And when you plug it into your calculator, you do find that it is indeed lower than 1 ,000.
04:01
We get 873 .1 oms for the total resistance of the entire circuit.
04:11
So we can call that part a.
04:16
For part b, we would like to find the current across r1.
04:21
And we know that r1 is 1 ,000 oms.
04:29
And we also know that for a parallel circuit, that each branch will have a voltage drop equal to the battery that is parallel with.
04:41
So both branches will have a voltage drop of 12 volts.
04:46
And so the current i1 will equal what? well, we can use oms law.
04:55
We have v is equal to ir.
04:59
And so i1 will be equal to the voltage drop across r1, which is just going to be 12 volts because it is the only resistor in branch a divided by the resistance of r1, which is 1 ,000 oms.
05:20
And so we get that the current i1, which i will draw.
05:27
Here.
05:28
So we have this current, i1, and then we have some current going in the other branch, i2.
05:38
So we get that i1 is 0 .0137 amps.
05:49
And i'm rounding a little bit, so you might see a slightly different numbering your calculator, but it won't be too different.
05:55
For part c, we would like to find the total current in the entire circuit.
06:02
So now we want i total...