Basically, can someone help me with this: http://www.alpharubicon.com/altenergy/understandingAC.htm ? What are the EXACT physics behind it?

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In the first graph, the power and current are exactly in phase, so the average power is maximized and it is always positive.

In the second graph, the voltage and current are 90 degrees out of phase, and therefore the power is lower, and the average power is zero.

Capacitors cause voltage to lag current (why?) so they are used to "correct" the power factor by placing the voltage and current back into phase.

i= CdV/dt - an inverse of the relationship for an inductor.

In what circumstances are you talking about power and power factor ? Having currents etc at some non-zero phase to voltage is useful and important in some systems.

Now, in a capacitor, you can't get a CURRENT through the capacitor, without voltage charging its plates. How does that ELECTRIC field create a CURRENT....

i=Cdv/DT

All of this is part of the general topic of electromagnetism. You are one fairly small step away from me invoking Maxwells equations to explain much further - which virtually stem from the observed phenomena in inductors and capacitors. For my second year degree course in EE, we had 2 hours to prove Maxwell's equations from first principles.

HTH

Steve

rate of changeof flux changes. V=Ldi/dt IS true by definition, since as we already know dPhi/dt is directly proportional to di/Dt. .For fundamental AC theory, I remember teaching myself (with some help from my father) from old Radio amateur books - they're great for a qualtitative view of the principles.