Switching charge between capacitors in a lossless circuit.
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Another source is SOUND energy caused by the arc during make.Emission of an EMW is the only thing which can consume energy.
Why is it infinite?Dissipated heat is equal to E^2 / R, and is therefore infinite. We can capture the dissipated heat and use it to make HHO gas for running our cars.
Yes but if you have a 0 ohm resistor then it won't dissipate any power.Because the assignment foolishly specifies R = zero.
I think it's rather more than that and taught in respectable electrical engineering texts. Students should be aware that there is a loss of energy from the system, with or without resistance.This old problem is nothing more than a slight-of-hand trick.
When any switch is closed arcing occurs, minute or larger scale. This dissipates energy. The calculation about the resultant steady state shows the system to be in a lower energy state as TNK observed.
However the system is not lossless as stated.
I agree. This problem, or thought experiment, can teach a couple of good lessons. The interesting thing is that, what was once a thought experiment is no longer unrealistic since the discovery of superconductors.I think it's rather more than that and taught in respectable electrical engineering texts.
Why do you say impossible? What if we do the experiment in vacuum and rapidly close a mechanical switch?It is impossible to avoid arcing as one brings two charged contacts (even mercury wetted ones) closer and closer. When they are microscopically close, but not touching, the electric field is intense.
Imagine two conductors, one connected to the charged capacitor, one connected to the uncharged capacitor. They are widedly separated, but connected at their other ends to the common connection between the two cpacitors.Why do you say impossible?.....
Unfortunately, it is a pay-to-read journal and I cannot give a workable link to the full article.We discuss the two-capacitor problem found in many introductory physics texts in which there appears to be missing energy in an ideal, zero-resistance circuit, following the sudden charging of one capacitor from another. The paradox of this missing energy is traditionally ascribed to finite-resistance wires, the initial assumption of an ideal circuit and the rapid nature of the charging
notwithstanding. By treating radiative effects in the simplest approximation, we show that the paradox is really nothing more than an inappropriately applied lumped-parameter model. In
particular, we show that in the zero-resistance circuit, radiation fully accounts for all of the energy lost. To explore radiative effects in more realistic circuits, we also discuss numerical examples that
include a small resistance and inductance.
Yes. This is why my suggested thought experiment said to work in vaccum and bring the switch closed very radidly. If the switch closes faster than a significant number of ions can leave the surface, then not all of the missing energy can be dissipated in a microarc.If there is no intervening matter, at some closer, but still non zero, separation the field will be strong enough to cause particles to leave the surface of a conductor, either as electrons or ions, thus establishing the current that forms the mcro arc.
by Aaron Carman
by Jake Hertz
by Jake Hertz
by Jake Hertz