Finding the voltage of a circuit

[x86]

Homework Statement

Capacitor 3 in Figure (a) is a variable capacitor (its capacitance C3 can be varied). Figure (b) gives the electric potential V1 across capacitor 1 versus C3. The horizontal scale is set by C3s = 20 μF. Electric potential V1 approaches an asymptote of 10 V as C3 approaches infinity. What are (a) the electric potential V across the battery, (b)C1, and (c)C2?

http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c25/fig25_44_wiley.gif

Homework Equations

C=q/V=(permitivity constant)A/d

The Attempt at a Solution

I've been stuck on this problem for 1 hour. I just can't figure it out. I can't figure out the voltage of the battery, which is supposed to be 10V.

What I've tried to do is look at when C3=infinity which means that the distance between the capacitor is 0, so its just a wire. Then I get a parallel circuit with C1, and C2, where the voltage going through C1 is 10V. This makes a series circuit with C1, C2. So I know that the voltage of the battery = 10V + the voltage through C2. I can't figure out how to get 10V for the battery

 

[TSny]

What I've tried to do is look at when C3=infinity which means that the distance between the capacitor is 0, so its just a wire. Then I get a parallel circuit with C1, and C2, where the voltage going through C1 is 10V. This makes a series circuit with C1, C2. So I know that the voltage of the battery = 10V + the voltage through C2. I can't figure out how to get 10V for the battery

I'm not following where you state that C₃ = $\infty$ makes a parallel circuit and then in the next sentence say it's a series circuit.

Can you derive a general expression for the voltage V₁ in terms of the battery voltage, V, and C₁, C₂, and C₃? You can then see what happens as C₃ goes to infinity.

 

[NascentOxygen]

What I've tried to do is look at when C3=infinity which means that the distance between the capacitor is 0, so its just a wire.

While that concept of it being "just a wire" might work for you in most situations, rather than "distance being 0" it may be better to think of plate area being huge.

As TSny points out, your narrative is confused/confusing, so you need to get that sorted out.

I think you should sketch your own copy of the graph that is provided, but this time label the horizontal axis in uF not their confusing C_3s nonsense.