Why is the Charge on the Equivalent Capacitor the Same as C1?

[Strawberry]

Homework Statement

Q17. Capacitors C1 and C2 are connected in series and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

A. the charge on C1

Homework Equations

q = CV
1/Ceq = sum ( 1/Ci )

The Attempt at a Solution

Well the answer is given, but I don't understand it. I keep doing the problem according to the formulas, but I get q1*q2 / q1+q2

 

[alphysicist]

No, that does not look right. I think the place where you are going wrong is maybe you are thinking that $q_1=C_1 V$. (This is not true because C1 does not have the full battery voltage V across it--part of it is across C1 and part across C2.) What is true is that $q_1 = C_1 V_1$.

So what is the charge on the equivalent capacitance in terms of C1,C2, and V?

Once you have that, you can find the charge on C1 by itself.