Patrick Leonard said:

I'm studying electrical engineering and I've learned that inductors and

capacitors introduce a -/+ 90 degree phase shift between the voltage and

current. But lets look at an inductor with just a single loop - no tricks

here, just a wire that loosely forms a single turn (pick up your mouse cord

and try it). Such an arrangement most certainly does not produce a 90deg.

phase shift. I'm sure you can see where I'm going with this - at what point

does an inductance cause a 90-deg. phase shift in a circuit? Presumably,

for any given frequency, w, there would be a particular inductance

(ultimately, a particular geometry) that would be required for a full

90-deg. phase shift. Is what I've said so for correct? Does the magnitude

of the inductance have some correlation to the magnitude of the phase shift?

(It must...)

In that case, how does one calculate the 90-deg phase shift inductance?

If this is true, why is that inductors are modelled as |x|<90 in phasor

notation (ie, magnitude of reactance at an angle of 90) -- as this will

ALWAYS yield a 90-deg. phase shift in circuit analysis...despite the fact

that the inductor, may not in fact produce such a phase shift!

As noted, this is something I'm studying but don't really understand.

Please feel free to use math to explain.

PS. This is leading up to another question

Patrick,

Very good questions. It shows that you're thinking.

The phase relationship of the current and voltage in inductors and

capacitors is ALWAYS 90 degrees. They (*perfect* L's and C's) just don't

ever act any differently -- regardless of what type of signal is being

applied.

However, in the real world -- either by circuit design or due to intrinsic

flaws in the parts -- the net phase of the voltage and current may not be 90

degrees. For example:

Let's say you take a 3" piece of wire and loop it into a 1" (roughly)

diameter loop, and put a 1K ohm resistor in series with it. Now, connect a

sine wave (constant voltage) generator across the series combo.

Apply various frequencies -- let's say between 1Hz and 1MHz.

If you monitor the phase difference of voltage and current at the inductor

it would be 90 degrees. However, you would notice that the magnitude of the

voltage, across the inductor, would be VERY small with respect to the

applied voltage at the generator. This is the key idea, here.

The phase relationship of the voltage/current (V-I) at the generator will be

(almost) 0 degrees. This is because the majority of the voltage drop is

across the resistor, and the V-I phase of a resistor is 0 degrees. So, the

resulting (vector sum) of the I*R drop of the resistor, and the I*2*pi*f*L

drop of the inductor will be a voltage/current phase relationship of

(nearly) zero.

If you were to increase the generator's frequency to a larger frequency,

let's say where X(subL)=2*pi*f*L = 1K ohms, then the phase of the voltage

and current, at the generator, will be 45 degrees. Increase the frequency

even more and the phase will keep increasing, and will eventually approach

90 degrees.

Remember, while all these different frequencies are being applied, the phase

of the voltage/current at the inductor has ALWAYS been 90 degrees.

Keep thinking. It WILL pay off.

Bob