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Veritasium "How Electricity Actually Works"
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ejeffrey:

--- Quote from: electrodacus on May 13, 2022, 04:47:24 pm ---
--- Quote from: timenutgoblin on May 13, 2022, 12:50:02 pm ---The pathological nature of the Two Capacitor Paradox problem leads to the observation that only the Law of Conservation of Charge is satisfied, but the Law of Conservation of Energy is violated.


--- End quote ---

Law of conservation of energy has never been broken/violated.  There is no paradox related to the two parallel capacitors so that page on Wikipedia is misinformation as anyone can write a wiki page and write whatever it wants.

--- End quote ---

Of course.  And you absolutely need to stop saying that other people on this thread are claiming conservation of energy is violated.  That is just an outright lie and it isn't ok.  Stop it.

The point of the paradox is to show that the initial setup is non physical.  Postulating zero loss and zero inductance and requiring that you reach a steady state is a non physical setup and the equivalent to dividing by zero.  Any conclusions drawn from it are meaningless.  Your entire premise is based on something that cannot exist and is meaningless.

With no inductance or resistance the voltage is discontinuous and the current flow is infinite.  That is impossible.  If you add any finite resistance or inductance -- even an attohenry everything becomes finite and does not agree with your claim.  This is trivially verifiable analytically, by simulation, or by experent.
TimFox:
Even "dividing by zero" can be handled analytically with proper limits.
As an example, the famous sinc function
y=sin(x)/x obviously goes to 1 at x=0,
even though both the numerator and denominator are 0 at x=0.
electrodacus:

--- Quote from: ejeffrey on May 14, 2022, 07:52:48 pm ---
Of course.  And you absolutely need to stop saying that other people on this thread are claiming conservation of energy is violated.  That is just an outright lie and it isn't ok.  Stop it.

The point of the paradox is to show that the initial setup is non physical.  Postulating zero loss and zero inductance and requiring that you reach a steady state is a non physical setup and the equivalent to dividing by zero.  Any conclusions drawn from it are meaningless.  Your entire premise is based on something that cannot exist and is meaningless.

With no inductance or resistance the voltage is discontinuous and the current flow is infinite.  That is impossible.  If you add any finite resistance or inductance -- even an attohenry everything becomes finite and does not agree with your claim.  This is trivially verifiable analytically, by simulation, or by experent.

--- End quote ---

You will be spiking for yourself in regards to energy conservation as it seems many people disagree with that either knowingly or unknowingly like Derek did in the Direct downwind faster than wind video where what he basically presented there was an overunity device so getting more power out than in.

You can not get rid of inductance but you can get rid of resistance.
And you can get inductance as a intermediary energy storage in a normal circuit with resistance and reduce the effect of energy loss as I already demonstrated very close to ideal case of zero energy loss that is possible for a circuit with no resistance.

The two capacitor problem is useful if understood to debunk the main claim Derek made and that is the "energy doesn't travel in wires".
All energy including the initial transient (AC) and the DC after that will travel from the source to the load (lamp/resistor) through wires.
There is absolutely no evidence of Derek's main claim and he's supposed evidence is to show that there is energy arriving at the lamp before the electron wave had the time to travel the entire transmission line about 65ns in his experiment.
The explanation for that small amount of energy he sees before those 65ns is easy to explain if you understand that a transmission line is made of distributed capacitance and inductance elements for the entire length of the transmission line and that the capacitance being an energy storage device is the one responsible for that current seen through the lamp while energy is stored in the two capacitors each side of the lamp.
There is no current flow through a capacitors when charging but there is a current flow in to a capacitor and that just means energy travels through wires as electrical energy is the integral over time of electrical power which is the product of electrical potential and electrical current.
Since current is not possible through the dielectric of a capacitor in this case 1 meter of air electrical energy can only travel through wires.
IanB:
A question (for Tim, ejeffrey, or whoever):

How do we precisely define the circumstances in which conservation of charge is applicable when analyzing a system, and when it is not?

For example, we may have capacitor A holding a charge Q0, terminals connected to one side of a black box. A second capacitor B starts out uncharged and is connected to the other side of the black box. The black box draws power from capacitor A and uses it to charge capacitor B. At the end of the process, capacitor A has remaining charge Q1 and capacitor B has charge Q2. We can imagine that Q1 + Q2 may not always be equal to Q0.

We know that if the black box just contains a series resistor, then conservation of charge will apply. But if the black box contains a DC/DC converter, then maybe not.

What is the rigorous technical statement about when and where conservation of charge applies? Is it related to the number of closed loops in the system topology? That conservation of charge applies around each loop? But then what about branches where two loops overlap? Or is it that conservation of charge should apply within each separable island in the topology, such as on each side of a transformer?

Or is this just overcomplicating things, and one should just apply KCL around each node in the system and sum over all the nodes?
hamster_nz:
I would love to hear electrodacus's analysis of the behavior of this circuit when the switch is closed, with Vi of 3 V and C of 3 F, with ideal capacitor, wires and switches, of course, (so no dissipative elements).
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