For the system of capacitors shown in figure find a the...

For the system of capacitors shown in Figure, Find (a) the equivalent capacitance of the system (b) the potential across each capacitor (c) the charge on each capacitor (d) the total energy stored by the group.

Transcript

00:01 All right, here we have a fun circuit problem and our goal at first to find the total equivalent capacitance.

00:09 So notice we have two parallel strands, each of the strands are series.

00:15 So it's going to be made up of the capacitance.

00:18 I will write it as the top strand in parallel with the capacitance of the bottom strand.

00:26 But those are in parallel with capacitors they add.

00:30 So let's find the capacitance of the top strand and the bottom strand and then we'll add them together.

00:36 Okay, the capacitance of the top is going to be product over some because there's in series.

00:42 So three micro ferrets, six micro ferrets over three micro ferrets plus six microferrets.

00:53 And so we ended with 18 over nine or two microferds.

00:57 So that is see at the top.

01:00 This is what i'd call the top part.

01:02 Then this part is the bottom.

01:05 Okay, so see at the bottom then, this bottom half is going to be product over some, but we have two micro ferrets and four microferds.

01:15 And then we're going to add the two capacitancees on the bottom.

01:21 All right.

01:21 So that's going to give us eight over six or four over three microferds.

01:27 So if we go back up to the top equation, see at the top, let's see at the bottom.

01:31 We can now add those two values and we'll get our total capacitance.

01:38 So our total capacitance is 10 thirds microferrets, which is 3 .33.

01:45 Anyway, 10 thirds.

01:47 All right.

01:47 So good.

01:48 That was part a.

01:50 I'm going to go ahead and do part c before b.

01:53 I think it's a little easier.

01:55 So let's do part c next.

01:57 Part c has to do with finding the q or the charge in each of the capacitors.

02:07 And i think this is pretty easy because the q is always the same along any series pass.

02:13 So the q, i'll call it q3 microfarrid capacitor.

02:18 Is this going to be the same as the 6 microferred capacitor? and it's the same as just thinking of it as the charge on the top.

02:27 So all those will be the voltage across the top times the capacitance of the top.

02:33 But we already know those values.

02:34 All of them have 90 volts across.

02:37 Our capacitance at the top is two microferreds.

02:40 So that goes pretty fast.

02:41 We get 180 microcoules and that is for all the capacitors on the top.

02:49 So now let's do the capacitors on the bottom half...

Question

For the system of capacitors shown in Figure, Find (a) the equivalent capacitance of the system (b) the potential across each capacitor (c) the charge on each capacitor (d) the total energy stored by the group.

Please give Ace some feedback