I don't understand U=0.5CV^2 - seems to be incorrect formula!

[OldN00b]

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!

[albert22]

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.

That should be:
0.5 * 8 * 100 * 100 = 40000 Joules
because you now have 8 farads instead of 4

[OldN00b]

Oops, sorry and thank you for explaining!  :-)

So there is no multiplication of charge.. I was just making calculation errors? Hm.. My mother was right - I should have been killed when I was still a baby :-)

Part of my confuzzlement was because I had assumed that the formula for caps in series was something different from the reality..

[T3sl4co1l]

That's not charge, that's energy.

Charge is Q = V*C.

Parallel capacitances add (the voltage remains constant), and series capacitances reduce (the harmonic mean, i.e., the reciprocal of the sum of reciprocals; voltages add).

If you combine these three facts (and the energy equation), you will find things do, in fact, make sense.

Tim

[OldN00b]

Thanks. I did not know that there was a difference between charge and energy. I will look this up, now..

[LukeW]

As charge flows into a capacitor, the voltage across the capacitor increases.

The energy of each charge quantum is qV, but the energy on each charge quantum keeps changing as the capacitor charges up, so to find the total amount of energy stored in the capacitor we basically want to integrate V(q) dq from 0 to Q, where Q is the total final charge on the capacitor.

The definition of capacitance C is Q / V, and V(q) is equal to q / C.

So we integrate (1/c) q dq from 0 to Q, and that's where we get E = (1/2C)Q² from.

Substitute Q = CV into that, and we have E = 1/2 CV² as expected.

[OldN00b]

Thank you :-)