# Series / parallel capacitor network: find two capacitances and source voltage given some measured data

Capacitor 3 in Figure (a) is a variable capacitor; its capacitance $$C_3$$ can be varied. Figure (b) gives the electric potential $$V_1$$ across $$C_1$$ versus $$C_3$$. The horizontal scale is set by $$C_3 = 20 \, \text{μF}$$. Electric potential $$V_1$$ approaches an asymptote of $$10 \, \text{V}$$ as $$C_3$$ approaches infinity.

What are

(a) the electric potential $$V$$ across the battery,

(b) $$C_1$$, and

(c) $$C_2$$?

equations: $$C=\frac{q}{V}=\frac{A}{\epsilon_0 d}$$

How does one solve for the voltage on the battery, which is supposed to be $$10 \, \text{V}$$?

What I've tried to do is look at when $$C_3 = \infty$$ which means that the distance between the capacitor is 0, so its just a wire. Then I get a parallel circuit with $$C_1$$, and $$C_2$$, where the voltage going through $$C_1$$ is $$10 \, \text{V}$$. This makes a series circuit with $$C_1$$, $$C_2$$. So I know that the voltage of the battery is $$10 \, \text{V}$$ + the voltage across $$C_2$$. I can't figure out how to get $$V$$ for the battery.

When $C3=\infty$, when you combine it in parallel with $C2$ you have infinite capacitance, which means zero voltage. When you combine that in series with $C1$ you just have $C1$, so all the battery voltage is across $C1$