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# Paradox of charged capacitors

Paradox of charged capacitors ... why law of conservation of energy or charge are both valid yet gives different solutions of final voltage, when a charged cap is connected across a discharged cap.

#1

11-29-2013 01:13 AM

Top #2

It's a paradox only if losses are ignored. Yes, it's a paradox with ideal components, but those don't exist.

You get another paradox if you add a small inductor in series. Envision opening the switch again when the inductor current goes to zero, and analyze your results.

You get another paradox if you add a small inductor in series. Envision opening the switch again when the inductor current goes to zero, and analyze your results.

11-29-2013 03:35 AM

Top #3

can a capacitor remain

charged in isolation, if yes, how long?

charged in isolation, if yes, how long?

11-29-2013 05:44 AM

Top #4

@Ganesh: didn't get ∆U =

U0 C2 / C1 + C2 Of particular interest is the case for large C2 (C2 → ∞), where all stored energy is lost. Does this mean if C2 is large a fully charged C1 will never be able to deliver charge on it? What will be the case if C2>>C1 so that C1 can be ignored. regards, Anand.

U0 C2 / C1 + C2 Of particular interest is the case for large C2 (C2 → ∞), where all stored energy is lost. Does this mean if C2 is large a fully charged C1 will never be able to deliver charge on it? What will be the case if C2>>C1 so that C1 can be ignored. regards, Anand.

11-29-2013 08:32 AM

Top #5

Has anybody considered the phenomenon of dielectric storage, particularly under discharge conditions? The dielectric PVDF is a good example of this property . .

11-29-2013 10:34 AM

Top #6

Hiring manager at my current position threw that one at me after I had breezed thru all of his tough questions. The answer is that the 'lost'energy is radiated out as EMI.

11-29-2013 01:11 PM

Top #7

Hi Dave .......Thats what I thought too , and also the reason why I found this paper interesting and posted this to the forum .

When one cap discharges into another, under ideal conditions.... Zero Resistance => Infinite Current in Zero Time ...... This is like the impulse function and the first thing that comes to mind of practical engineers is that the lost energy is due to radiation.

But this paper analyses this abstraction and actually goes on to prove that the lost energy cannot be due to radiation! .............His example on expanding the plates of the capacitors where again there is an energy loss paradox , but without connecting wires , so no flow of current and no radiation possible !

When one cap discharges into another, under ideal conditions.... Zero Resistance => Infinite Current in Zero Time ...... This is like the impulse function and the first thing that comes to mind of practical engineers is that the lost energy is due to radiation.

But this paper analyses this abstraction and actually goes on to prove that the lost energy cannot be due to radiation! .............His example on expanding the plates of the capacitors where again there is an energy loss paradox , but without connecting wires , so no flow of current and no radiation possible !

11-29-2013 03:46 PM

Top #8

Hi Anand,

That is precisely the paradox .

Finite charge on finite capacitance gives a finite voltage across capacitor, hence finite energy.

Now if this finite charge (energy) is dumped onto an infinite capacitance, then voltage across the infinite capacitor , then V=Q/C = finite/infinite ........ which mathematically means zero voltage and hence zero energy , so all energy is lost.

As Edward said, this is a paradox only with ideal components which practically dont exist. If there was a finite resistor in the circuit, it would not be a paradox any more.

That is precisely the paradox .

Finite charge on finite capacitance gives a finite voltage across capacitor, hence finite energy.

Now if this finite charge (energy) is dumped onto an infinite capacitance, then voltage across the infinite capacitor , then V=Q/C = finite/infinite ........ which mathematically means zero voltage and hence zero energy , so all energy is lost.

As Edward said, this is a paradox only with ideal components which practically dont exist. If there was a finite resistor in the circuit, it would not be a paradox any more.

11-29-2013 06:24 PM

Top #9

Expanding the plates transfers energy to/from the mechanical system.

11-29-2013 08:43 PM

Top #10

Assuming zero resistance is akin to dividing by zero. Both can lead to bad conclusions. As pointed out at an APEC conference, the value of the resistor makes no difference in the end states - just the timing.