# Circuits - using equivalent capacitance

1. Jan 28, 2012

### shawli

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

C1 = 1μC ; C2 = 2μC ; C3 = 3μC ; C4 = 4μC
V = 12.0V

If both switches are closed, what is the charge on C1?

2. Relevant equations

q = CV

In parallel - V is constant across capacitors
Cxy = Cx + Cy

In series - q is constant across capacitors
Cxy-1 = Cx-1 + Cy-1

3. The attempt at a solution

I'm REALLY lost with this circuit.
This is what I broke it down to:

(C1 || C2) in series with (C3 || C4)

And then I attempted to work backwards from there, but I can't seem to get the correct answer (which is 8.40μC).
I added rough sketches of the circuit I was trying to break this down into... Not sure if I'm even on the right track!

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2. Jan 28, 2012

### Staff: Mentor

Are C1 through C4 meant to represent capacities (microfarads) or initial charges (microcoulombs)? Units make a difference!

Assuming that they are actually capacities in μF,
That's good. What values did you get for C12 and C34?

Are you familiar with the voltage divider equation for series capacitors?

3. Jan 28, 2012

### shawli

Sorry - the "C" means capacitor, I should have clarified in the question!

Is this the voltage divider equation? http://www.electronics-tutorials.ws/capacitor/cap_7.html I've been trying to read up on this stuff but no, I don't actually know what it is haha.. (have yet to cover it in class)

I got C12 = 3μF and C34 = 7μF (because you simply sum up voltage across parallel capacitors right?).

I then got Ceq = 2.1 μF (taking C12 to be in series with C34).

4. Jan 28, 2012

### Staff: Mentor

Yes, that page depicts the concept quite well. For the case of just two capacitors in series you can just remember that the total voltage across them divides inversely as the individual capacitances. So if capacitors Ca and Cb are in series and have total voltage E = Va + Vb across them, then
$$Va = E \frac{Cb}{Ca + Cb} ~~~~~~\text{and}~~~~~~Vb = E \frac{Ca}{Ca + Cb}$$
That's correct. If you can determine the voltage across the capacitor that you're interested in (C1) then you can determine the charge on that capacitor from your formula q = CV. The voltage across C1 must be the same as the voltage across C1||C2, which you can determine with the voltage divider concept.

5. Jan 28, 2012

### shawli

Ah, got it! Thank you :)