A homework problem asked me to find the voltage across a series of capacitors after they came to equilibrium.
Essentially a capacitor C1 with a capacitance of 6.0 F is charged until the potential difference (V) is 9.0V across it using a battery.
This battery then is removed and replaced with a second uncharged capacitor C2 with a capacitance of 3.0F. The goal of the question is to determine the voltage across C1 after the system has came to equilibrium.
The answer is that C1 has a voltage of 6V across it however in solving this problem a number of questions came up. And a number of different ways of solving it came up.
One way of getting to that solution hinges on the assumption that the voltage across capacitor 1 needs to be equal to the voltage across capacitor 2 and thus their q/C ratios should be the same. We are not sure whether this conclusion is correct.
This results in us having some confusion about the potential difference across capacitor 2 at the end. And then if the potential difference does not add up at the end can we even use Kirchhoff's laws since the potential difference in the system is 9 and thus there wouldn't be a point where the sum is 0?
To explain the confusion here are some diagrams of our thinking. Are we even right about our assumptions of the potential difference of the system?