00:01
Okay, so for this question, we've got a circuit with resistors in series, and then we'll tackle a circuit with resistors in parallel.
00:09
So the first part, we want to find the equivalent resistance for the circuit.
00:13
So for resistors in series, which is what we have here, the equivalent resistance is just the sum of all the resistances that you have.
00:21
So since we have five here, i'm just going to write r1 plus r2, plus r3, plus r4, plus r5, and then we'll substitute in all the values that we have for those resistors.
00:35
So four of them are 20 oms, so i'm just going to write that as 4 times 20, and then r5 is 10.
00:43
So that would give us 90 oms for the equivalent resistance.
00:49
Then we want to find the current through each resistor.
00:53
So the current, since they're in series, the current through each resistor is going to be the same, and it's also going to be the same as what we could consider the total.
01:01
Total current.
01:02
So we're going to use olms law first.
01:05
I guess we're really only going to use own law once.
01:07
So i'm going to write out what i just said.
01:10
So i total is equal to i1, which is equal to i2, which is equal to i3, which is equal to i4, which is equal to i5.
01:21
And this comes from the fact that they're in series.
01:24
And then we can get the total current.
01:27
Let me move this up a little bit to give myself some space.
01:30
We can find the total current, using the total current, using olmslaw, so we'll have v total, which is just that 9 volts being provided by the battery, is equal to i total times the equivalent resistance.
01:44
That guy's 9 volts.
01:47
The equivalent resistance we found to be 90.
01:50
So then we'll divide both sides by 90, and then i'll kind to go to the right over here.
01:57
And then 9 over 90 is going to be 0 .1.
02:00
The unit for current is amps and then that will be the current that is going through each resistor.
02:08
Now for the potential drop across each resistor, that's not going to be the same.
02:14
So we're going to have to use olmslaw for each resistor using the current that we just found and the individual resistances.
02:23
So i'll kind of set them all up.
02:25
So we'll have v1 is i1 times r1, v2 is i2 times r2.
02:36
B3 is i3 times r3.
02:39
I guess i'll start plugging this in.
02:41
So i1 is equal to i total, which is that.
02:44
R2 was 20.
02:46
So this will give us two volts.
02:53
The r2 is equal to r1, so is r3, so is our four actually.
02:58
So these are all just gonna be two volts.
03:01
So i'll try and get through writing these out a little quicker.
03:07
B4, i4 times r4, again, 0 .1 times 2, or times 20 is going to give us 2.
03:17
And then b5 is i5 times r5, which was 0 .1 times 10, which is 1 volt.
03:27
And then if you were to add up all those voltages, it would come back equaling the total voltage that we had being provided by the battery.
03:35
So you could always give yourself a check.
03:39
Then for the power dissipated by the resistor, so we do have, and then we want the power supplied by the battery.
03:46
So we can say power is equal to current times voltage.
03:50
We'll use that equation to get the power supplied by the battery.
03:55
And again, these two values should end up being the same.
03:58
And then when we're interested in power dissipated across the resistors, you plug in for v in that equation for power, um, olms law, and you get a relationship that is power is current squared times r.
04:12
So we're going to use that i squared equation for the individual resistors, and then we'll use p equals iv for the battery.
04:20
So hopefully this will all fit.
04:22
So p1, i1 squared r1, 0 .1 squared times 20.
04:31
So i'm just going to, plug that one into my calculator, just double check.
04:35
Okay, so that comes out to be 0 .2, and the unit for power is watts.
04:44
So, again, the current and the resistances are the same for resistors 1 through 4, so i'm not going to redo the math.
04:50
I'm just going to write down what they are.
04:54
It's all the same math as what i just did for p1.
04:59
And then i'll try and squeeze down here, but p5, that's the one that's going to be different, so that one i'll write out...