The charge in a capacitor is 0.5 times the capacitance multiplied by the square of the voltage. OK. Simple.
Here comes my great bewilderment:
Say I have 2 caps, each 4 Farads, each charged to 100 Volts. I connect them in parallel. The total charge is 0.5 * 4 * 100 * 100 = 20000 Joules.
Now say I connect those same caps (already charged) in series.
1/Cv = 1/4 + 1/4 so Cv = 2 Farads.
The total voltage is 100 + 100 = 200 V.
The total charge is 0.5 * 2 * 200 * 200 = 40000 Joules.
This implies that the formula to calculate stored charge in a capacitor is incorrect, because by simply disconnecting my cap from its parallel circuit and connecting it in series, I miraculously double the total stored charge, which would violate the law of conservation of energy, effectively creating energy out of nothing.
Please explain to me where I'm making a mistake.
I'm working on a project, trying to store as much charge as I can (it's for a particle beam weapon - just kidding). Attached look what I've done to some 2000 V caps. I'm still soldering more of these "sandwiches" :-)
Thanks!