i've done a reasonable amount of circuit analysis, both AC and DC and i've never used the term dq/dt for current.
can you explain to me what i'm missing?
What Trippy said:, add the total number of Coulombs passing through a node for one second, and that tells you how many Amperes are flowing. I brought this up because Layman believes a capacitor can charge (thereby elevating the voltage across the terminals) without current flowing.
My main point is that we can measure the available energy at the output of his circuit by E=qV, where q is the Coulombs of available charge sitting at V volts. That can never be greater than or equal to the energy used to produce the charge at that voltage in the first place, due to conservation of energy. Notice that Power = dE/dt = d/dt(qV) = (dq/dt)(V) = Vi. It may seem a little pointless, but it's always good to walk through relations like this to double-check units, and to reinforce basic concepts. Both are lacking in Layman's approach to design.
For some reason Layman went into a Creationist argument, or something of that sort, trying to say that, if the universe came from nothing, then conservation of energy was violated, therefore he can violate it at will, and produce free energy, simply by arbitrarily picking components and wiring them together as he sees fit. That puts him in a very cranky position to be engaging folks here on questions of electrical engineering.
As a side remark, since the main issue here is energy, I would strongly suggest that everyone who ever actually wanted to understand the limitations on technology, insofar as energy is concerned, begin by creating a chart that illustrates all the forms of energy you can think of. For example, here I have explained that E = qV but of course I could write that several other ways, e.g., E = P × t = Vi × t. Continue this as a list of categories and you'll keep thinking of more forms until you eventually run out of ideas:
Categories of energy:
Static electricity: E = qV
Electric current: E = Vi × t
Planetary gravity: E = mgh
Linear kinetic: E = 1/2 mv²
Torque: E = τθ
Pneumatic: E = PV (ideal gas law)
Thermal: E = nRT (ideal gas law)
Wind: E = 1/2 At
ρv3
Electrochemical: E = qV (from table of half cell reactions, using mass of electrode erosion × valence to get q)
:
and so on. Then you can quite simply estimate the max available energy from any machine or device that converts energy from one form to another. Of course if you take every permutations of these, you end up with some odd kind of machines, such as one that uses a falling weight to pressurize a gas, or one that uses static electricity to produce wind. And so on. But a few of these, the ones that apply to steam turbines and generators, are of great interest, as well as the limits on batteries and renewable sources. Of course these are only upper limits based on idealizations. In practice, the designs become very complicated as you attempt to make them more and more efficient.