Note that the original posting that started this discussion (and which seems to have been lost from this thread) described a problem that was in the sinusoidal steady state, and therefore required only the use of reactance and Ohm's Law (because reactance is measured in ohms) for solution. Only one of a perverse nature would lead the OP along to the unnecessary terrain of transient behavior and differential equations.
Look at the OP's first post again. The title of the thread was I = C dv/dt, and he asked how to obtain dv/dt. That is a differential equation question, not a steady state condition.
There is a well-respected contemporary author whose thesis is, "The World is Flat".
Which is easily disproven by any picture taken of the Earth from space.
[Current flows. Learn the language or be labeled a stubborn curmudgeon.
Charge flows, current already means flow. Don't have to say it twice. Don't use technical slang when precision is valued.
Also, if current did not flow through the capacitor dielectric then there would be a discontinuity in the current, and that cannot happen.
You are TTT again. If current existed through the capacitor, it would be leaky. Capacitors that are leaky are discarded. If a capacitor did not store a charge on one of its plates and dispense an equal charge on its opposite plate, how could it store energy? How could it exhibit reactance and an exponential curve for the current when a constant voltage is applied?
That is why Maxwell's equations include a "displacement current" proportional to the rate of change of the electric field in the dielectric. Current flow is not caused only by the movement of charge but also by a changing electric field.
I am quoting from a book called Introduction to Electrodynamics
, Third Edition, by David J. Griffiths.
"Maxwell called his extra term the displacement current
It's a misleading name, since it has nothing to do with current, except that it adds to J
in Ampere's law."
Do you know what you are talking about?
The two "circuits" are not isolated but rather connected by the displacement current.
You are way out in left field. The dielectric is impermeable to charge transport. The only inside connection between the plates of a capacitor is an electric field which appears when the plates have unequal charges.
It can also be said that the charges (electrons) that enter a wire are not the same charges that exit the wire. Ever hear of 'drift velocity' of electrons in a conductor? So tracking the identity of individual charges in a capacitor is a bogus concept.
Let me make it clearer. The charges next to one side of the dielectric will never cross to the opposite side of the dielectric.
A capacitor does not store charge. A fully charged capacitor contains no more electric charge than an uncharged capacitor.
A capacitor does not store net
charge. However, one plate does store a charge and, the opposite plate depletes its charge by the same amount, for a net change of zero.
Mesh Analysis and Nodal Analysis are unconcerned with what may happen inside a connected device. A resistor, a capacitor, or an inductor are just two-terminal devices having a simple mathematical description of the voltage-current behavior at the two terminals.
Isn't that what I said in the last post? The mathematics of mesh analysis do not discern that a capacitor accepts charge into one terminal and releases an equal amount of charge at the opposite terminal.
That depends on how deep you want to go into understanding what is happening.