0:00
All right, hello.
00:01
In this question, we're given this circuit diagram with these values.
00:04
And we're told initially the capacitors are uncharged.
00:06
Then the switch is thrown to position a, which is the left position.
00:11
And we're asked, after a long time, what is the charge and voltage on each of the capacitors? so if they're initially uncharged, we know that for capacitor 2, it's going to stay with that same initial charge, right? because capacitor 2 isn't actually connected to the battery at all.
00:27
It's connected to the negative terminal.
00:28
But there is no way for charge to flow from the battery across this gap and into capacitor 2.
00:36
So capacitor 2 doesn't have a voltage going across it when the switch is in position a.
00:42
So its voltage is going to be 0 volts.
00:45
And it was initially uncharged, so it's going to remain uncharged.
00:48
So that's for 2.
00:50
For capacitor 1, we have basically this diagram here.
00:55
So we have q is our c1 over here.
00:57
We have v here.
00:58
And this is when the switch is in position a.
01:00
This is essentially what's happening.
01:03
So if we know that this has a voltage v across it, we know that we must also have a voltage v across this.
01:10
So vc1 here is going to equal v.
01:12
And we're told that is 12 .5 volts.
01:16
And then what is the charge? well, we know that the charge on a capacitor q equals c times v.
01:21
So we have our capacitance.
01:24
It's 145 times 10 to the negative 6.
01:27
That's a microfarad times our voltage of 12 .5 volts.
01:32
And so if we go ahead and do that calculation, we're going to get the charge is 1 .81 times 10 to the negative 3.
01:40
And the charge is in coulombs.
01:41
So we could also write that if we want as 1 .81 millicoulombs.
01:47
Either one would work.
01:48
But that will be the charge across capacitor 1 when the switch is in point a.
01:53
I'm then told that i'm going to flip the switch after a long time.
01:56
So after this capacitor fully charges up, i'm going to flip the switch to b.
02:01
So i'm going to go ahead and throw the switch to the right here.
02:05
I'm assuming that that is b in the diagram that's labeled as c.
02:08
But i think that's just a drawing error.
02:11
And so when i do that, i'm going to have this circuit here.
02:14
I have c1, which is directly connected to c2.
02:20
And those are not connected to the voltage source at all.
02:23
Well, i know that this voltage here initially, so v0 of 1, is going to be just the 12 .5 volts...