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# How does an inductor cause current to lag voltage in the case of an alternating current, and why is this bad?

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

## Discussions

Inductance isn't "BAD" at all ! Its just a natural consequence of electrical physics. The voltage across an inductor depends on the rate of change of magnetic flux inside it. V=n x d(phi) /dt. Since the flux inside the inductor depends on the current passing through it, V=n d(i)/Dt. If the current is sinusoidal, i=Ipk x sin(wt), then V is proportional to w x Ipk x cos(wt).

I'm not saying that Inductance is "bad", I'm asking why current lagging voltage is a bad thing. From what I could tell, it causes power loss, but the more important question for me is how exactly the inductor does this, and you nailed it.

It does NOT cause power loss per sae, what it CAN do is increase the losses in a system where there is a non-unity power factor. Again, current lagging voltage is not bad in itself though.

From what I could tell, because P=VI, you can construct the following graphs:

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.

The voltage across a Capacitors lags the the current because in a capacitor

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.

Which kinds of systems is it useful in? From what I've gathered, the power company is doing a certain amount of work, but as the voltage and current begin to drift out of phase, they are forced to do more and more work to get the same amount of power to the consumer. In this way, it is bad for the two to be out of phase, because the power company spends more money to get the same amount of power to the consumer.

In power systems, there are times when power stations have to produce pure VA rather than Watts for network reasons. Non unity power factor doesn't mean they have to generate MUCH more power, they just have to supply more current, which makes slightly higher losses in the cabling. In electronic filter circuits, we rely on phase lags and leads to get the output we want. AC induction motors NEED a capacitor to start them, which causes the magnetic field in the stator to rotate relative to the rotor.

Thank you, but can you explain "V=n x d(phi) /dt" for an inductor and "i= CdV/dt" for a capacitor EXACTLY? I understand that this is true, and it does answer my question, but what is the explicit mechanism for this? Thank you.

What have you got in an inductor ? A coil of wire. What can you get in a coil ? You can't get a voltage across its terminals unless a current flows, and that will create a magnetic field. How does that magnetic field "set" the voltage ? ....by that mathematical relationship.

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

Sorry, to fill in your previous question, dphi/Dt - rate of change of flux inducing voltage. dV/Dt rate of change of voltage proportional to rate of change of charge per unit time. charge changing is a current.

The problem for me is not with the mathematics, I understand them perfectly well, and everything looks good on paper, can you please help me by explaining the particle interactions inside of an inductor? From what I can gather, electrons flow through the coil, thus generating a magnetic flux (phi) if the voltage is changing (and it does with AC). Then, by Lenz's law, this expanding flux (during the first part of the cycle, when the voltage is rising) causes a reverse current to be induced in such a way that the flux it generates opposes the flux generated by the main current. The net current is thus negative. However, when the voltage peaks and begins to drop, the magnetic field begins to collapse, and thus current is induced to oppose this negative flux, and it is induced in the direction that the main voltage would have it go, so it adds to the net current. In this way, voltage and current vary with voltage being proportional to the derivative of the current. My questions are, is this correct, and why is exactly must this proportion (V=L*dI/dt) be true?

You've got most of it right. There is only one field in the core though. Think of currents rather than electrons. Not so much "expanding" flux as "increasing" flux, creates more back -emf as the

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.

To read about the EXACT physics behind the electrical and magnetic properties of inductors, I suggest that you do an internet search for information from more authoritative sites than this forum of primarily amateur respondents. You could start by visiting wikipedia @ www.wikipedia.org and enter "inductor" in the internal search bar at that location. On that note, I'll dispense with the mechanical analogy and the magnetic interpretations and leave the rest to you.

Reread the paragraph starting "In electric motors". I think that's about as good an explanation as you're going to get without spending a couple of semesters in class.