# Homework Help: Charge stored in a capacitor

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1. May 10, 2017

1. The problem statement, all variables and given/known data

Question : How much charge is stored on the capacitor C2 ?

2. Relevant equations

Q = C . U

3. The attempt at a solution

Since Q2, the charge stored on the capacitor, is C2 . (Va - Vb) , I thought that I just had to multiply 1.0 x 60 = 60.
But in fact, the expected result is 40, how ??

2. May 10, 2017

### CWatters

Your equation Q=CV is correct but the voltage V is the voltage across the capacitor. Does all of the 60V appear across C2? How much of the 60V appears across C3//C5 ?

You haven't mentioned C1 but it can be ignored. Why?

3. May 10, 2017

The potential difference across C1 is 0 since C2 = C4 and C3 = C5.
I have thought about the fact that the voltage across C2 may be incorrect, but in that case how can I find it ? Kirchhoff's law doesn't seem to help in this case

4. May 10, 2017

### CWatters

Correct.

You can simplify the circuit to two capacitors in series C2//C4 + C3//C5. Then you assume the capacitors start off discharged when the voltage is applied. There will be a rush of current as they become charged. Since they are in series the current (eg charge) that flows through both capacitors is the same.

5. May 10, 2017

So if we have Ca = C2 + C4, the charge stored by that capacitor will be q = 2 x 60 = 120, right ?? But then what do I do ?? Isn't it the same thing that I had tried in my first attempt ?

6. May 10, 2017

### epenguin

Since you have realised there is no charge on C1 you can ignore it, rub it out, everything is the same as if it were not there.
Then in parallel you have two branches which are exactly the same. Essentially they are independent. You are only asked something about one of them. So the problem is exactly the same as if you had only that branch. Two capacitors in series.

Then you can mechanically use the formula for that which I don't encourage, except maybe as a check at the end to see everything is the same however you work it out. Or you could think: the charges aon the two capacitors are the same, so from Q = CV, as the Q's are the same what's the ratio of the voltages across them? That will give you the voltage across the capacitor C2, and the charge on it.

You can practically do this problem in your head. In more than half of the capacitor or resistor networks given as problems on this forum, there is simplifying feature of a symmetry. Which would cut down on calculation. But the students have been intimidated or brainwashed or something and can only think of doing it in a heavy plod way, formulaically, missing out even some of the simpe physical insight, even after solving.

I would also disagree with the question when it says "write out as a decimal".... The component parameters are usually given as whole numbers, so write answers as rational numbers. Because that is exact! Then at the last convert into a decimal if required.

Last edited: May 10, 2017
7. May 10, 2017

I see now, so at the end, we will have the two capacitors C2 and C3 in series, which we can consider as a single capacitor Ca = 2/3.
By applying Q = Ca . V, we have :
Q = (2/3) . 60 = 40.
And since the two capacitors does have the same charge, C2 has a charge of 40. Is it correct ??
Thank you very much

8. May 10, 2017

### epenguin

Yes I0W, in fact IW, since C2 has half as much capacitance as C3, to hold the same charge it needs twice the voltage across it as C3, so two thirds of the total voltage, so 40 V, so gets (with 1 μF capacitance) 40 µC of charge.

Re another point I made, you see that even the "rounding off" request was intended to confuse.

9. May 10, 2017