Unraveling the Mystery of Phase Differences in Passive Circuits

[es1]

The what is the fact the i is being restricted by the R. As the cap changes V the R changes V too.

 

[wbeaty]

That is not how physics or even engineering works.

Nope. That's exactly how physics works. See the book "The Character of Physical Law," the section about Babylonian approach to physics. A bit of it is online in various places:

http://www.google.com/search?q=babylonian++feynman

But in double-E, we only need the math models. To do design, we have zero need to understand the internal physics of components. An equation is enough, and "understanding" is not the goal. So perhaps the real problem is that this is the EE section of bbs.

It seems that asking physics questions here just makes everyone annoyed and defensive, since it's not their area of expertise, so they don't know how to answer.

 

[wbeaty]

What and how is causing the overall of 56.3

How about this.

You're OK with the physics behind a capacitor having 90deg leading current, right? (not lagging.) And a resistor has 0deg in-phase current? You understand the physics behind both of these?

Well, if you hook a resistor in series with a capacitor, and connect this whole thing to a sinewave voltage generator, the circuit will draw a current that's somewhere BETWEEN 0deg and -90deg phase. And by changing the resistor and capacitor values, you can adjust the current phase to anything you want, between 0 and 90.

Where does the non-zero phase come from? From the capacitor. (After all, it's the only thing in there which can contribute a phase-shift!)

 

[IssacBinary]

Thanks for backing me up wbeaty.

But I think your right, its probably the wrong place to be asking. But to me its not like I am asking for a super in depth on quantum, just what's happening in the circuit.

EE guys seem to be fine in explaning what's happening in a capacitor, with the electrons, repealing one of the other plate, they build up bla bla bla...but that's more than just saying "90 degrees" so I don't really see the problem with my question.

So, this is what I am come up with so far, an AC source, resistor and capacitor all in series...

1) Higher the frequency the shorter the time the capacitor has to charge up, meaning less voltage across the capacitor at its maximum.
2) once the voltage after the resistor is less than what the capacitor is charged up to, the capacitor starts to discharge
3) Due to higher frequencys meaning the capacitor has less charge and less voltage, for it to be able to discharge it needs to wait longer for the AC source to meet the capacitors voltage and go less. This would mean there would be MORE than a 90 degree lag with the discharge. As say the AC source peaked up 10V and the capacitor only charged to 2V then it has to wait to almost the end of the cycle for it to be able to discharge (when AC source reaches back down to 2V and less).
4) the combination of the capacitors discharge smaller voltage going left + the original source voltage going right add together (superposition) to create a final resultant voltage in the circuit of a certain amplitude and phase.

Thus a 56.3 shift as per my example. Which is dependent on frequency and capacitance to calculate reactance which is point 1, 2 and 3, and reactance I had explained without maths in a few posts before...

I realize this explanation is not 100% spot on, but I think its a long the right path but needs to be tweaked...

Hopefully this makes people realize what kind of explanation I am after.

 

[sophiecentaur]

Right, but now we are back at a capacitor.

Im asking for an explanation that uses the cap to create an overall phase shift in the circuit.

The shift in the cap is 90 degrees but the total impedance - overall phase shift - in the circuit is 56.3.

What and how is causing the overall of 56.3

The 'reason' for the arbitrary looking phase shift is that the voltage across the supply is shared between C and R and the R governs the amount of current flowing into the capacitor and the voltage across it.

 

[sophiecentaur]

To those who say that, somehow, Maths is an invalid way to approach 'understanding' I offer the following.
Maths, spoken language and Dance are all languages which are used to communicate ideas. If you reject Maths for a good explanation of the way a capacitor, in favour of a spoken description, then why not reject a spoken explanation in favour of an explanation delivered through the medium of Dance?

 

[IssacBinary]

Im not saying maths in invalid, but using ONLY maths and saying that maths is all you need to understand is what I am saying is not right.

Even though my problem isn't directly about the capacitor on its own...

If dance was able to act out what's happening inside a capacitor. As in the dancers where to move and act out electrons moving and they stop in one place and gather up to show a charging capacitor...

then the person watching it would see this and be able to relay it in words and physically happenings.

then from this you can see patterns and derive the mathematical model that governs all these actions and performance..

So, if an explanation could be delivered through dance that's makes someone understand their problem then sure, that would be great. Anything to help in gaining an understanding is always positive, no matter how its delivered.

But again, this is slightly irrelevant. As the problem I am asking for help on isn't some kind of philosophical question or something that doesn't exist.

Maths on its own isn't going to explain why something is happening. It can tell you what's happening and where etc but not why...yes it can tell you why but not a why in a sense of "now I understand what is happening so now the maths makes sense".

But can't we work together to help me and my problem?. What part of the 4 steps is wrong in my explanation in post #34?

 

[wbeaty]

To those who say that, somehow, Maths is an invalid way to approach 'understanding' I offer the following.

Feynman's "Babylonian" explanations are saying that? Really?

So, because Feynman describes himself as a Babylonian, you conclude he's one of a group who says Maths is invalid for understanding?

I think you misunderstood the "Babylonian" material.

 

[es1]

Im not saying maths in invalid, but using ONLY maths and saying that maths is all you need to understand is what I am saying is not right.

Who is saying that? We're saying you start with the physical model of a resistor & cap (V=IR & Q=CV), then apply math to it. One needs both the model and the math. Only math won't be sufficient to solve the problem. You're basically trying to construct a new model for some reason and many of us don't understand why.

But can't we work together to help me and my problem?. What part of the 4 steps is wrong in my explanation in post #34?

The high level problem is it seems to me you have two different models of a cap. One that has a zero reaction time (this is the one used to make the reactance and the 90degree) and one that has a finite reaction time that takes time to react to a frequency. It's not clear how to predict the reaction time before hand and which model is the right one to use for a given circuit.

In step 1 I'll assume you meant to add, for a given fixed current. Otherwise we could have the same dv in less dt by simply upping the current. (Hopefully this rings a bell as to what effect the series resistor is having.)

In step 2, the voltage relative to ground at the output end of the resistor is the same as the voltage on the cap.

In step 3 it is not clear why anything needs to wait longer than the source. And since charge is proportional to voltage in a cap, why is frequency involved? When one is less the other is less without needing to resort to a time interval.

In step 4: I don't really follow it. I am not sure why there are two voltages inside the cap and why superposition applies.

 

[es1]

I thought of a new way to describe it, some, but minimal math.

Vs=voltage at source, Vc=voltage at cap

Because of the presence of the series R there is a max I that can go to the cap to charge it for a fixed Vs. Because I is bound, as dt goes down (or frequency goes up) dv must go down for a given C.

To charge the cap the equality Vs > Vc must hold. To discharge the cap, Vc > Vs must hold. Because |Vc| is changing with frequency but |Vs| is not the time where we flip from one equality being true to the other changes with frequency, thus phase changes with frequency. Different Rs & Cs create different bounds and therefore different crossover points.

I have to admit I am not 100% happy with this but I think it's the best I can do.

 

[f95toli]

It seems that asking physics questions here just makes everyone annoyed and defensive, since it's not their area of expertise, so they don't know how to answer.

Well, I am a physicist; not an EE guy. The only reason I post in this section quite frequently is that I am experimentalist, and most of my experiments involve electrical measurements (+design of some of the equipment) so I need to know a thing or two about electronics.
Also, although I've spent most career working on device physics I do know a thing or two about the microscopic theory of electrical transport; which is why I know that there is no easy "physical " answer to this question (I actually did my PhD working on the effects of the d-wave symmetry in high-Tc superconductors on the current-phase relationship, so I literally spent several years thinking about "phase").

1) Higher the frequency the shorter the time the capacitor has to charge up, meaning less voltage across the capacitor at its maximum.
2) once the voltage after the resistor is less than what the capacitor is charged up to, the capacitor starts to discharge
3) Due to higher frequencys meaning the capacitor has less charge and less voltage, for it to be able to discharge it needs to wait longer for the AC source to meet the capacitors voltage and go less. This would mean there would be MORE than a 90 degree lag with the discharge. As say the AC source peaked up 10V and the capacitor only charged to 2V then it has to wait to almost the end of the cycle for it to be able to discharge (when AC source reaches back down to 2V and less).
4) the combination of the capacitors discharge smaller voltage going left + the original source voltage going right add together (superposition) to create a final resultant voltage in the circuit of a certain amplitude and phase.

Thus a 56.3 shift as per my example. Which is dependent on frequency and capacitance to calculate reactance which is point 1, 2 and 3, and reactance I had explained without maths in a few posts before...

If this is the level of understanding you are looking for that is fine (since you are not actually referring to the microscopic theory, which is why I thought you were looking for). However, I still don't understand why you think this is any easier to understand this text than just looking at the formulas and working through the math yourself? Math is a language created to deal with problems like this, and what you wrote above can be be written much more easily using it.
My suggestion would be to sit down and calculate the voltage and current at every point in the circuit, once that is done you can draw the waveforms, this will hopefully give you a more "intuitive" picture if that is what you are after. Another way of doing it would be to play with a SPICE program such as LT Spice (which is free, it can be downloaded from Linear's website); this is an excellent education tool.One of the signs of "maturity" when it comes to solving problems and understanding phenomena in physics is to be able to look at the the math and "understand" it, without having to "translate" it to English. This becomes more and more important as the material becomes more advanced, until you reach a point where it is all you got (i.e. when you start dealing with quantum mechanics etc; which quite literally no one understands).

 

[sophiecentaur]

The word 'understand' is not easily defined. At best it means that one has enough grasp of a situation to be able to predict further and extrapolate. At worst it can mean nothing at all- or even a complete lack of a valid idea. It is frequently no more than 'that feeling' of confidence about a topic.
I cannot think of a great Physicist or Engineer who got there without a lot of Maths with the ability to interface that with the physical world at each end of the maths.
The notion of 'what is really going on' lost it's validity when New Science came along. Just think of all the quotes about QM and understanding. They apply to us all but Maths gives us a better chance of advancing than waving our metaphorical arms.
You could possibly demonstrate a simple process with dance but could you really expect to solve a problem that way? Is there a way to 'speak' Maxwell's equations and then derive, verbally, the wave nature of light?
Those who want science without maths are like people who emigrate yet never bother to take on board the language and culture of their new home. They just don't get the full experience.

 

[DragonPetter]

I really like this thread, I hope you keep prying into the explanation OP. But can you think of examples of phase that aren't about capacitors? Can you explain how you get arbitrary phase differences then? I don't think it is magic, or a purely abstract idea, and so you should be able to draw parallels and bring ideas back to the capacitor situation.

Have you considered the imaginary component of the voltage you are applying to the capacitor? Remember there is one. Have you looked at this problem in terms of the complex plane and how all of this plays its role in phase?

 

[sophiecentaur]

I love that post. How could that question be raised without maths? Rofl
Just proves my point.

 

[Evil Bunny]

Entertaining thread here...

Why do folks feel the need to dictate how someone wants to go about learning something?

Keep that train rolling... I love to see people getting down to a real understanding... however they want to get there.

Regurgitating equations reminds me of politicians reciting their talking points.

The math is obviously required, but if someone wants more to help make it stick, I think that is very important.

Don't let them discourage you... Keep digging until it makes sense!

 

[wbeaty]

1) Higher the frequency the shorter the time the capacitor has to charge up, meaning less voltage across the capacitor at its maximum.
2) once the voltage after the resistor is less than what the capacitor is charged up to, the capacitor starts to discharge
3) Due to higher frequencys meaning the capacitor has less charge and less voltage, for it to be able to discharge it needs to wait longer for the AC source to meet the capacitors voltage and go less. This would mean there would be MORE than a 90 degree lag with the discharge. As say the AC source peaked up 10V and the capacitor only charged to 2V then it has to wait to almost the end of the cycle for it to be able to discharge (when AC source reaches back down to 2V and less).
4) the combination of the capacitors discharge smaller voltage going left + the original source voltage going right add together (superposition) to create a final resultant voltage in the circuit of a certain amplitude and phase.

Very important:

• Beware of falling in love with your own creations.
  
• Instead, create several different ones. That way if one of them proves bogus, the blow to one's ego isn't as large.

If your explanation contains a fatal flaw, you'll have to throw the whole thing out and start over from scratch.

To be a physicist is to become your own worst critic. (It's a bit like being an author who commonly is required to kill off major characters.) NEVER try preserving your own creations by cultivating blindness to mistakes. Go over it with a fine tooth comb repeatedly, and keep looking out for death-blow type errors.

 

[f95toli]

Why do folks feel the need to dictate how someone wants to go about learning something?

Experience? Age? Because we'v been there?

One thing that makes Physics Forums a bit different from most of the forums on the internet is that quite a few of the members actually know what they are talking about, as opposed to just expressing random opinions.
Hidding behind many of the handles are actual scientists, engineers, professors etc who have spent years working in various fields of physics and engineering. Moreover, many of us have also taught science at one level or another. I worked as a TA when I was a PhD student, and therefore spent about 1 day a week for 5 years teaching among other things a lab course in basic electronics (including an introduction to AC circuits). Hence, it is not the first time I've come across this question. Moreover, I've seen plenty of students trying to "understand" things in electronics without the math and I therefore know how pointless it is in the long run.

 

[IssacBinary]

Regurgitating equations reminds me of politicians reciting their talking points.

The math is obviously required, but if someone wants more to help make it stick, I think that is very important.

Thank you :). Like I said. IM NOT REJECTING MATHS. I can do the maths, I can answer and work out problems fine. But just maths alone won't let you understand what things mean, what is happening.

Think way back to when electricity was first being discovered. People observed what was happening, did experiments to see how things where working then after lots of repeats, patterns came about and then the relationships and formulas where derived.

But the biggest thing is.
Everyone seems fine explaning how a capacitor works in terms of moving electrons. Electrons enter one side, the field repeals them from the other side, you get an imbalance on the plates thus creating a voltage.

That kind of explanation you see in the books and taught at school etc and that explanation has NO MATHS. But no one is whining about that.

Then from that you MOVE onto the formulas and maths. Change in charge = differentiation etc and you learn the relationships and formulas...Fine...good.

I also understand that there are very abstract ideas, although I havnt studied Maxwells equations yet, I still stand by my idea that things can be explained without maths. Differentiation is...Maths...yet that can be explained without maths.

many of us have also taught science at one level or another

This is nothing against anyone on this site. But just because your a teacher obviously doesn't mean your good at actually teaching. there's good and bad teachers, but at the same time they maybe both know their subject equally well. So I don't really see that as a "reason".

See Walter Lewin's lectures for example...

In step 4: I don't really follow it. I am not sure why there are two voltages inside the cap and why superposition applies.

You miss understood, there is not 2 voltages inside the cap. That and "super position" is both explained in my drawing...

So back to my question, I've made a drawing (another way to communicate ideas) so maybe that might help people understand what I am after and what I am talking about.

 

[FOIWATER]

Just to clarify, obviously we all know what PHASE physically means... phase just refers to WHEN in time... and two waveforms shifted 90 degrees apart means they peak 90 degrees apart...

So is your question as simple as why does the current through a cap lead the voltage across it by 90 degrees (and you're looking for this explanation in a physical way, without numbers)?

Think first that the impedance value of a coil or cap is not the same as for a resistive element as it has an associated impedence attached to J (J simply being a place holder that rotates a vector 90 degrees within TIME). What this physically means, is that some of the current is not purely resisted, rather it seems impeded as it is used to form magnetic fields within these devices... such as the magnetic field within the plates of a cap, or through a coil...in a cap this rotation by 90 degrees is seen as negative ( -J ) since the current builds up a field in the dielectric..

the potential for the circuit exists, and we always assume it to be our reference... so we say it's in phase. Because the current through the capacitor is a function of the potential and the impedance ... and the potential is reference and it is an inherent characteristic of the cap to resist current in TIME to build a field... we end up with a shifted PHASE for our current waveform with respect to our reference potential.

I know this is basic stuff but honestly your question just seems to have been overlooked... maybe I'm 100% out to lunch but this is the best i can do without math..

 

[FOIWATER]

On second thought maybe my answer is too basic and you obviously know what I typed and you're asking, why 90 degrees?..where does that particular value come from? How is it achieved? In this case.. I might have to agree with Sophie in saying that 90 is a number and was arrived at by mathematical analysis..

Hope you find your answer... I'll keep reading hoping I learn too

 

[IssacBinary]

I know this is basic stuff but honestly your question just seems to have been overlooked... maybe I'm 100% out to lunch but this is the best i can do without math..

Exactly! And what you just explained was not my orignal question. I have said many times I UNDERSTAND the phase inside the capacitor.

Also many times I have explained my question and what I do want explained.

OVERALL PHASE SHIFT.

This post explains it the best.
https://www.physicsforums.com/showpost.php?p=3377063&postcount=19
Then read this post
https://www.physicsforums.com/showpost.php?p=3381323&postcount=48
It has a nice big picture

 

[Evil Bunny]

Moreover, I've seen plenty of students trying to "understand" things in electronics without the math and I therefore know how pointless it is in the long run.

I'm sure you're very smart and a good teacher. Obviously there are plenty of folks on this board who know much on the subject, but you're still missing the point.

He's not trying to understand things without the math... He has repeated himself over and over again that he understands the math. He has proven it with his examples.

He wants more explanation in addition to the math... I have pondered this very question and never bothered to ask about it. The math is easy here.

Some of us like to just think about things like this a little more. Spraying people with equations when they ask questions like this (and tell you repeatedly that they understand the math part of it) isn't helping anything. Telling them they're wasting their time and it's pointless to try to think of it that way comes across as being a little... well... arrogant.

Now maybe to you this is a waste of time, and that's fine... but try to understand everyone is not "wired" the same way, so to speak. There is more to understanding electricity than throwing math books at people. Just sayin...

 

[es1]

He wants more explanation in addition to the math... I have pondered this very question and never bothered to ask about it. The math is easy here.

I am not sure such an explanation exists.

Here is an analogy.

What if we defined phase as the length of a shadow (it is just an arbitrary definition of a physical quantity anyway). And then you said, "ok, but why is the shadow 10m long." And then we replied, "if you know the dimensions of the object and the light source position etc. you can use geometry to figure it out."

And then you said, "ok. I get how you worked that out. But explain why it is 10m without geometry."

How could someone do that? I don't think you could say why the shadow is 10m, and not say 9.8m, without geometry.

 

[es1]

Keep in mind the question was why is the phase shift X. An explanation that can't answer why the phase shift is X and not Y isn't going to work.

 

[sophiecentaur]

Exactly! And what you just explained was not my orignal question. I have said many times I UNDERSTAND the phase inside the capacitor.

But "Phase inside the capacitor" is a meaningless concept so I have a feeling that you don't in fact understand.

 

[IssacBinary]

I am not sure such an explanation exists.

Here is an analogy.

What if we defined phase as the length of a shadow (it is just an arbitrary definition of a physical quantity anyway). And then you said, "ok, but why is the shadow 10m long." And then we replied, "if you know the dimensions of the object and the light source position etc. you can use geometry to figure it out."

And then you said, "ok. I get how you worked that out. But explain why it is 10m without geometry."

How could someone do that? I don't think you could say why the shadow is 10m, and not say 9.8m, without geometry.

Im not asking for an explanation to give an exact answer for an exact value for an exact situation.

But more of a general explanation.

i.e The harder you push something the faster it moves because for you to push harder you need more energy thus you have transferred more energy so the object is moving faster.

F = ma

...So for your example.

The closer the sun is to 90 degrees over your head the less the suns rays have to go from going past your head to the ground. So it makes a smaller length shadow.
If the sun is less than 90 degrees, say its almost straight on, then the sun rays have to go a lot further to get to the ground after touching your head because its more of a horizontal line of sight, so once it does reach the ground it makes a longer shadow as its had to go a lot further.
The space before where the sun rays touch the ground is the shadow.

Its general. But still an explanation, and then it matches in with the "why is it 10m?" "because of geometry"..."but why"..."because of the sun / light".....
Then once you understand the concept, the maths makes more sense. The maths sits on top of the non math explanation and your able to see why and what things now mean.
"Ohhh so that's why it gets smaller, and this is the formula / maths to calculate exact " Like 1 over big angle (between 0 - 90) = smaller shadow (1/x...bigger x is the smaller the 1/x is)...(that was just an example)

 

[wbeaty]

So all I am saying is. When we work out impedance I can see how the resistance / real part of impedance can be explained, like i just did, tug of war expample. But I am asking about the total impedance PHASE part. How is that created?

Note that the phase of current is *leading,* not lagging. I mean, when you apply a sinewave to your R and C in series, the current doesn't lag behind the voltage. It leads.

Your explanation has to end up with a leading phase. Negative degrees relative to the voltage driving the circuit. I think your present explanation predicts a phase lag, right?

Could this be a major sticking point?Going further: if we connect a capacitor directly to a sine-wave voltage generator, what happens? Remember, NO SERIES RESISTOR. The sinewave generator creates a voltage, not a current. The voltage gets applied directly across the capacitor terminals. The capacitor draws a current from the supply, similar to the way a 120V light bulb draws a current from distant 60Hz generators. What will the capacitor current look like? (Again, it's not 'the capacitor-charging current creates a voltage.' That concept can't help us.)

Instead we have to go backwards, starting with voltage.

 

[wbeaty]

I am not sure such an explanation exists.

Definitely right: these types of explanations simply don't appear in textbooks. Search forever, and you won't find this one.

So we'll have to sit down right here and construct it ourselves.


(Or, did you mean that such an explanation is impossible? Nah, I created this style of explanation all the time back in science museum work. "Teach physics to little kids and grandmothers." In physics exhibits you can't fall back on any math whatsoever. The general public education level is ~grade 6-7, and they're all math-hating/phobic. You can't rely on "Latin," you'll have to translate it into "gutter-slang" i.e. words and pictures. Animations. Animations help lots!)

 

[wbeaty]

But "Phase inside the capacitor" is a meaningless concept so I have a feeling that you don't in fact understand.

Phase of the current wrt the applied voltage. The current is inside the capacitor, so the phase is "inside."

But yes, he might be missing something big: that a capacitor's current doesn't only charge the capacitor. That's only half the concept.

The other half: a changing capacitor voltage will draw a current from a power supply, and the faster the capacitor voltage is changing, the higher is the current.

 

[IssacBinary]

Note that the phase of current is *leading,* not lagging. I mean, when you apply a sinewave to your R and C in series, the current doesn't lag behind the voltage. It leads.

Your explanation has to end up with a leading phase. Negative degrees relative to the voltage driving the circuit. I think your present explanation predicts a phase lag, right?

Could THIS be a major sticking point?

No not really. If I get my lagging and leading mixed up it wouldn't really matter too much (some say it does)

But yes. The -56.3 from my early post would mean voltage is -56.3 behind current.

But again the way I see it, but just is never said this way is that I like to think of it as resultant voltages / currents.

As there's multiple things happening to create an overall end result.
In this case, TOTAL impedance is the overall "resistance" the circuit "seems" to have due to the effects of the capacitor and resistor together. Along with a phase shift.

The phase shifted current isn't coming out of thin air, its being created by a voltage that is in phase with it, but its a "resultant" voltage because its made up of different "happenings" in the circuit. So my guess why its never explained this way is because this "resultant" voltage is neither the source voltage or voltage across the capacitor.