Finding the charge on a capacitator

[Dell]

3 capacitators, C1=8μF C2=4μF C3=8μF, are connected in a colum, over a potential difference of 12V, what is the charge of C2??

i know that connecting the capacitators in a colum, ΣC=(Ca*Cb)/(Ca+Cb)

also i know that
C=Q/V, which i think must be the equation i need since i am looking for Q, but i don't think the V i know is the right V, i think its the V for the whole system.

ΣC_1,2=(C1*C2)/(C1+C2)=(8*4)/(8+4)=(8/3)μF

ΣC_1,2,3=(C3*C_1,2)/(C3+C_1,2)=(8*(8/3))/(8+(8/3))=2μF

so now i know V_total=12V and C_total=2μF

C=Q/V
Q=C*V
Q_total=2*12=24μC

but how do i find Q2 from the Q_total

 

[Cyosis]

The V is indeed the potential difference over the equivalent capacitor.

Do you know why capacitors in series add up like 1/C=1/C1+1/C2+...+1/Cn? Imagine at the very start the first plate of the capacitor is getting charged. What will this do to the plate below and the plate below and the plate below etc?

 

[Dell]

a sort of chain reaction, 1st will charge 2nd will charge 3rd... so they will all have the same charge?? meaning that
Q2=(1/3)*Qtotal

Q2=Q3=Q1=8μC

is that right?

 

[Cyosis]

You're almost right. The chain reaction you describe is correct and indeed all three capacitors have the same charge. However this charge is not 1/3 of Qtotal.

Lets call the potential difference over the first capacitor V1, over the second V2 and over the third V3. Using your chain reaction argument we know that Q=Q1=Q2=Q3. We also know that in series V=V1+V2+V3 and we know C=Q/V.

Now let's calculate them separately:
V1=Q/C1
V2=Q/C2
V3=Q/C3

V=V1+V2+V3=Q(1/C1+1/C2+1/C3). Looks familiar? Now calculate this Q and see that Q1=Q2=Q3=Q=Qtotal.

 

[Dell]

so it would probably be easier to just work it out like that from the beginning instead of adding up all the C's,,
thanks