Find Excess Charge on Capacitor 2 Given 10V Battery & 5x20µF Capacitors

[DivGradCurl]

In the figure attached, the battery has a potential difference of 10 V and the five capacitors each have a capacitance of 20 µF. What is the excess charge on capacitor 2?

I go inside out from the capacitors in series C_2 and C_3. My notation simply denotes the equivalent resistance depending on the type of connection (series/parallel).

C_{S1}= \left( \frac{1}{C_2} + \frac{1}{C_3} \right) ^{-1}

C_{P1}= C_{S1} + C_4

C_{S2}= \left( \frac{1}{C_{P1}} + \frac{1}{C_5} \right) ^{-1}

C_{P2}= C_{S2} + C_1

It also follows that

Q_2 = Q_3 = Q_{S1}

V_4 = V_{S1}

Q_5 = Q_{P1} = Q_{S2}

V_1 = V_{S2}

So, I get

Q_2 = Q_{S1} = V_{S1} C_{S1} = 1.0\bar{6} \times 10^{-4} \mbox{ C}

which is wrong! Could anybody please help me find the mistake?

Any help is highly appreciated.

 

[daniel_i_l]

How did you get Vs1? It isn't 10V, because some of the voltage goes to C5,
if you correctly found the Vs1 and just didn't show the work then it looks right to me.
I would find the Qs2 = Qp1 and then find how much Q goes to the different parts of p1 - how much of Qp1 goes to C4 and how much goes to s1.

 

[DivGradCurl]

I think I finally have it! I worked backwards from the desired result and used some relationships to guide me through.
Q_2 = V_2 C_2 = Q_{S1} = V_{P1} C_{S1} = \frac{Q_{S2}}{C_{P1}} C_{S1} = \frac{VC_{S2}}{C_{P1}} C_{S1} = 4 \times 10^{-5} \mathrm{ C}
Is this correct?
Thank you

 

[DivGradCurl]

I've just tried that result in my online homework page, and it works!