Why is it that, in the two capacitor paradox problem, the two capacitors are connected in
parallel with each other and the switch connected in
series as shown in the circuit below?
Source: Wikipedia en.wikipedia.org/wiki/Two_capacitor_paradoxWhy not have the capacitors connected in
series with each other (back to back, of course) and the switch connected in
parallel? After the switch is closed, the net voltage across the two capacitors will be zero since both capacitors would be equally charged and zero current would then be flowing.
I don't think it would make any difference to the initial and final charge/energy calculations.
Also, are the capacitors regarded as ideal voltage sources or ideal current sources? The fact that the capacitors lose/gain voltage and charge when the switch is closed suggests that they are (ideal) current sources and not (ideal) voltage sources.
\$I = C \frac{dV}{dt}\$ suggests that for a constant current the terminal voltage of a capacitor must either increase or decrease depending on the direction of current flow (assuming that capacitance is constant and NOT infinite).
In order to prevent the terminal voltage of the capacitor from decreasing the capacitance would need to be decreasing to maintain a constant voltage because voltage is energy per unit charge \$V = \frac{E}{Q}\$
If the charge on the capacitor is decreasing then \$\frac{dQ}{dt} < 0\$
Also, if the terminal voltage is decreasing then \$\frac{d{^2}E}{dQ{^2}} < 0\$
The output power is zero before the switch is closed, then peaks before both capacitors are charged and then returns to zero.
If the capacitors had infinite capacitance and were already charged to some voltage then the voltages of the capacitors would be constant across their terminals independent of flowing current. This is the definition of an ideal voltage source.
On the subject of mechanical analogies, there is a post in a related discussion thread:
https://www.eevblog.com/forum/projects/where-does-12-come-from-in-capacitor-energy-calculation/msg1671035/#msg1671035Using this mechanical analogy, it's as though the two capacitors
fuse together when the switch is closed as opposed to
colliding elastically where momentum and energy would be conserved.