AC Circuits and phase shifts

Suppose you have a resistor and capacitor in series. They have the same current, and their voltages add up to give the total voltage. One of those voltages is 90 degrees out of phase with the current, and the other is zero degrees out of phase. So the combined voltage is somewhere ** in between ** zero and 90.

Mark

On 5 Jun 2006 15:13:19 -0700, in message , "Mez" scribed:

Dang, well, the first thought that enters my mind is "do the vector addition and see!" Since that isn't going to work in this case, hmm, well let's see.

You understand that reactance is dependent on frequency, right? So let's pick 60Hz out of the air (really pretty easy to do ;-) and plug it into an inductor that gives 100 ohms reactance at that frequency. You already understand intuitively that the input to output voltage-to-current phase will be shifted by 90 degrees. Well now, let's put a 100 ohm resistor in parallel with our 100 ohm inductor, and let it take half of the current. The resultant phase shift is now half of what it was, because only half of the current is being shifted by 90 degrees, the other half not being shifted at all, and so the final result is a shift of 45, or half of 90.

The internal physics of how all that is happening is not really what's important toward understanding it intuitively, right? So all you have to know is that proportionate mixes of reactance and resistance will produce a final instantaneous result that may be obtained by algebraic calculation.

Howzat?

Well, I was going to say think it out, but...

...Then you understand that, when the voltage is changing fastest across a capacitor, the instantaneous voltage is, in fact, zero, but current on a capacitor is proportional to the rate of change, thus a capacitor has current maxima as voltage is crossing zero, or a 90° phase shift.

VECTOR ADDITION! LOL. Really, that's the truth, it's hard to put it any more succinctly...

If you want to analyze it stepwise, you can. But instead of analyzing a simple differential equation, you have the resistive term as well, which causes a bastardized equation, not quite resistive, not quite reactive. Which...is exactly what it is! But whatever the case, the solution really will end up looking like vector addition, with two orthogonal components and a Pythagorean looking term like Z = sqrt(R^2 + X^2).

Tim

simplest explanation i can give is the resistor deadens the effect of the reactance and makes it behave more like a resistor.

if you can put a negative resistance in there instead you get an oscilator :)

Bye. Jasen

Ah, and obviously adding two sinuses 90 deg. out of phase will result in a wave with the same frequency but 45 deg. shift. For some strange reason visualizing that was most of my problem... :) Thank you (and everyone) for that.

Here's another sort-of related question - Is it true that in order to acheive a maximum power factor I want to have an equivalent resistive-only impedance, such that the source sees no reactance - meaning, no phase shift relative to the source?

Yes. Reactance converts no energy ... canceling reactance makes the potential energy transfer 1:1. Classic example of this is power factor correction capacitors in industries with many motors that are inductive by nature and cause phase lag. Also, energy companies charge a penalty for lousy power factor ... which encourages industrial consumers to add power factor correction.

On Tue, 6 Jun 2006 18:58:53 -0400, in message , "Charles Schuler" scribed:

As further elucidation, allow me to offer that the power transmission industry spends a lot of effort and money to reduce power factor on their transmission lines (AKA Volt-Amps Reactive, or VARs - expressed as Mega-VARs if your system is big enough). Series and shunt capacitors, and reactor banks (the latter being inductive) are utilized to both reduce VARs and, less often, stabilize voltage level. The VARs don't produce power, so volt-amps dumped as reactive are wasted generation, AKA lost revenue.