# A circuit with three capacitors in series

Here is a picture of the given circuit. Initially the switch is connected to the left side, and the question is what are the charge and potential difference across each capacitor ( capacitance is in $$\mu F$$ ).

I want to make sure my understanding of this problem is clear. Here is my analysis. Before the switch is closed, all the potential from the $$100$$ V battery is stored into $$C1$$. After the switch is flipped to the right, $$C1$$ discharges some of its potential to $$C2$$ and $$C3$$, determined by their capacitances.

All three capacitors are connected in series, so $$C_{tot} = \Big( \frac{1}{C1}+\frac{1}{C2}+\frac{1}{C3}\Big)^{-1}$$

Giving way to explicitly calculate the voltage across $$C2$$ and $$C3$$. In this case the voltage is given $$V=(\frac{C_{tot}}{C})\cdot \Delta V$$. Where $$\Delta V$$ is the "total potential" = $$100V$$. In series, the charge across $$C2$$ and $$C3$$ is equal. However, the potential across $$C1$$ cannot be calculated this way, nor is the charge equal to the charge across $$C2$$ and $$C3$$. Instead, the potential across $$C1$$ is given via Kirchhoff's law : $$V1 -V2 -V3 = 0$$.

The role of $$C1$$ is certainly a bit different from the other two in this circuit, but I can't accurately explain why it behaves differently as it relates to the voltage and charge, even though it is connected in series with the other two. I think it is because $$C1$$ is the "source of voltage" in the right circuit. How exactly does $$C1$$ relate to the other two capacitors?

It is understandable that you assumed that the capacitors are in series. But notice that once $$C1$$ is charged, the top plate (assume for simplicity that these are parallel plate capacitors) of $$C1$$ is positively charged. And once the switch is flipped, the top plates of capacitors $$C2$$ and $$C3$$ are positively charged.
Now, because the positively charged plates of $$C1$$ and $$C2$$ are directly connected (and so are the negatively charged plates of $$C1$$ and $$C3$$), it is actually the case that $$C1$$ is parallelly connected to the combination of $$C2$$ and $$C3$$. Also, notice that it is indeed the case that $$C2$$ and $$C3$$ are connected in series because the negatively charged plate of $$C2$$ is connected to the positively charged plate of $$C3$$.