00:01
In problem 72, we're given that the emf is 72 volts.
00:07
The resistor r2 in the circuit diagram below has a value of 2 oms.
00:14
The capacitor c1 has a capacitance of 3 microfarids or 3 times 10 to the minus 6 ferrets.
00:22
And c2 has 6 microferred or 3 times or 6 times or 6 times 10 to the minus 6 ferrets.
00:28
The capacitor have obtained their final charges, so therefore they're assumed to be fully charged.
00:37
And when they're fully charged, c1 has a charge of 18 microtolums or 18 times 10 to minus 6 couloms.
00:47
And in part a, we're asked to find the charge on capacitor 2.
00:53
So i will be utilizing equation 24 .1.
01:03
So this is actually from the previous chapter where you're given that the capacitance is equal to the charge over the potential difference.
01:18
And in this particular case, these two capacitors are in parallel with each other.
01:25
And in that chapter in 24, when you have two capacitors in parallel, they have the same potential difference between them.
01:35
So let's write that c1 is equal to q1 over v.
01:43
So this is the common potential difference between the two capacitors in c2 is q2 over v.
01:54
And that's continue to solve this on the next page.
02:02
So i wrote previously that c1 is equal to q1 over v, and c2 is equal to q2 over v, because two capacitors are connected in parallel.
02:21
They have the same potential difference across them.
02:25
And from here, we can eliminate v.
02:30
Because we don't know v but we know c1 c2 and q1 and that will allow us to find q2 so and let's actually eliminate v from this equation then substitute into this equation so v from here is q2 over c2 and then we take this put it into this equation so that we have c1 is equal to q1 over q2 divided by c2 and let's just rewrite that a little bit.
03:18
C1 is q1 over q2 times c2.
03:32
And we actually want to find q2 so let's rearrange again so that we have q2 is equal equal to q1, c2 over c1.
03:52
And let's put in the numbers that we're given.
03:58
So q1 is 18 times 10 to the minus 6, coulums.
04:10
And then we have now c2, which is 6 times 10 to the minus 6 feralds divided by 3 times 10 to the minus 6 and this gives 36 times 10 to the minus 6 kulams or 36 microcoulons of charge so that answers part a in part b of the problem we're asked to find the resistance of the resistor r1 in the circuit diagram...