Unraveling the Mystery of Phase Differences in Passive Circuits

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SUMMARY

The discussion focuses on understanding phase differences in passive circuits, particularly involving capacitors and inductors. It highlights that in a capacitor, the current leads the voltage by 90 degrees, while in an inductor, the voltage leads the current by 90 degrees. The overall phase shift in a circuit is determined by the reactance of these components, which affects the total impedance and consequently the phase relationship with respect to the source voltage. The mechanics behind these phase shifts involve the time it takes for charge to move in capacitors and the self-induced EMF in inductors, which collectively create the observed phase differences in AC circuits.

PREREQUISITES
  • Understanding of AC circuit theory
  • Familiarity with reactance and impedance
  • Knowledge of phasors and sinusoidal signals
  • Basic principles of capacitors and inductors
NEXT STEPS
  • Study the mathematical derivation of impedance in AC circuits
  • Explore the concept of group delay in signal processing
  • Learn about the impact of non-linear phase shifts in control systems
  • Investigate the physical properties of capacitors and inductors affecting phase shifts
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Electrical engineers, students of circuit design, and anyone interested in the practical applications of phase shifts in AC circuits.

  • #61
IssacBinary said:
No not really. If I get my lagging and leading mixed up it wouldn't really matter too much (some say it does)

Not mixed up.

If your explanation predicts a lagging current, but the real current is actually leading, then your explanation has a huge flaw.

In physics-speak: your explanation is disproved by simple experiment.

IssacBinary said:
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.

Ah, that's the sticking point.

The phase-shifted current *is* coming out of thin air.

It's not being created by a voltage that is in phase with it.

This "resultant" voltage isn't in the circuit. It's not part of the intuitive/picture/verbal description.

It doesn't exist.

Let's get down to details. Why do you see a need for the "resultant" voltage? Is it because voltage causes current?
 
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  • #62
"is it because voltage causes current?"
Be careful not to make voltage into some kind of 'push'. Remember the actual definition of a volt. 1 Joule per Coulomb.
 
  • #63
wbeaty said:
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!)

This is very creditable stuff as long as you don't expect the kids and grandmothers to go out and be able to use these scientific nuggets for advancing Science any further. Great to get them into the subject (and for them to approve of taxes being spent on Science) but they'll still need the rigour and the Maths to build on what they've been told / shown.
 
  • #64
Thinking of voltage as a 'push' is a perfectly reasonable and logical way of analyzing circuits... In a non-math-hand-wavy sort of way. Makes perfect sense to us! o:)
 
  • #65
You carry on that way. Don't mind me. However, you risk falling on your face sometime if you do. "Hand waving" doesn't allow you to design or analyse even a simple electrical circuit, you'll find.
I guess you might also want to describe resistance as 'a sort of force stopping the current from flowing' (even worse!).
 
  • #66
Thinking of voltage as a push is not so far-fetched in the right context. Remember we can model entire mechanical systems with electrical circuit, because the same math applies to both systems.
 
  • #67
The bottom line of all this discussion is to ask the question - how many people who design circuits for a living and who make Engineering Systems work do it without Maths and by waving their arms about? There is no shame in finding Maths, at some level, difficult / impossible. But to dismiss Maths on the grounds that it doesn't reveal what goes on in complicated systems as well as analogies and hand waving, is totally missing the point. That just reads like inverted snobbery.
I totally take my hat off to people who's Maths ability is better than mine and wouldn't have the nerve to say that what they do with their maths is somehow lacking - which has been the flavour of several of the posts on this thread.
Throughout my technical life I have found that learning the 'next step' in Maths has given me an increased understanding of stuff that I may have felt, initially, I already had sussed.
 
  • #68
No one is arguing that you can explain this completely without math or that you shouldn't use math to describe the process. Of course, math and logic trump any intuitive explanation. But there is more to an understanding of physics concepts and especially engineering than pure math. There are a lot of artistic/creative aspects to circuit design and the math isn't always the first answer even if you end up using math in your final engineered design. Personal conceptions of how circuits work can help you use the right math tools.

Every physical thing should be explainable with math, but do we get out our calculators every time we want to know how much force we should use in our legs to sit in a chair or how many degrees to turn our steering wheel to make a turn? When we start to abstract everything with math, its easy to hide the physical processes.

And besides, most electrical engineering concepts are abstract models and don't necessarily represent what is really happening even if the math accurately describes the process. We don't derive maxwell's laws every time we calculate the current through a resistor, but we all know there is much more to the physical process and the mathematics than an equation that says V = I*R.
 
  • #69
IssacBinary said:
What is the mechanics that's causing the current at any point in the circuit to be out of phase with the source current.

This thread is too long for me to read through before midnight, but I hope someone has sorted you out on what I've quoted.

If for simplicity we consider a series circuit, then the current through every element is equal and exactly in phase with the current drawn from the power source. It's a series circuit, so the current at any moment in time is identical in every element. There is no phase shift in current anywhere in a series circuit.

In a series circuit, isource(t) = iR(t) = iC(t) = iL(t)[/color]
 
  • #70
sophiecentaur said:
I guess you might also want to describe resistance as 'a sort of force stopping the current from flowing' (even worse!).

Yeah... now you're getting it! It is kind of like that, isn't it? Not so much a "force" but more like a constriction or a road block type of thing getting in the way of those electron race cars that are zooming down the tracks :smile:

sophiecentaur said:
The bottom line of all this discussion is to ask the question - how many people who design circuits for a living and who make Engineering Systems work do it without Maths and by waving their arms about? .

Actually that's not the bottom line of this discussion at all... You have completely missed the point, even after it has been explained repeatedly.
 
  • #71
sophiecentaur said:
"is it because voltage causes current?"
Be careful not to make voltage into some kind of 'push'. Remember the actual definition of a volt. 1 Joule per Coulomb.


The question is, is IsaacBinary basing his reasoning on the idea that "voltage causes current?"
 
  • #72
I don't think it has been explained adequately that it's somehow better to hobble oneself by refusing to use a more powerful language. Why not try Latin with Roman Numerals at the same time?
 
  • #73
NascentOxygen said:
This thread is too long for me to read through before midnight, but I hope someone has sorted you out on what I've quoted.

If for simplicity we consider a series circuit, then the current through every element is equal and exactly in phase with the current drawn from the power source. It's a series circuit, so the current at any moment in time is identical in every element. There is no phase shift in current anywhere in a series circuit.

In a series circuit, isource(t) = iR(t) = iC(t) = iL(t)[/color]
Sorry. Maths alert. You aren't allowed to state it in that succinct way. ;-)
Wave your arms about a bit, if you want to be accepted.
 
  • #74
sophiecentaur, This is the last time I am going to say this point.

Am am NOT saying I CANT do the maths. I am not saying you DONT need maths. I am NOT saying I am stuck with the maths.

I am saying that ONLY using maths is not the way to get a full understanding.

As I've already demonstrated, I CAN use the maths.

I completely agree you CAN NOT design systems without maths.

Im saying that MATHS ON ITS OWN IS NOT going to explain what is happening.

The MATHS compliments an explanation of what's happening.

es1. I answered your question of explaining the geometry problem without maths.
https://www.physicsforums.com/showpost.php?p=3381555&postcount=56

But no one has commented to say either they see my point or disagree. It just seems like its been skipped even though that's what you asked me to do...

As per my orignal question and my example on my previous post. I am not asking for an explanation why the "total phase" is -56.3 and not -51.2. I am also not asking for an explanation for why its exactly them numbers.

Im ASKING for an analogy / explanation of what's going on to cause this effect. Then you apply the maths.
This thread is too long for me to read through before midnight, but I hope someone has sorted you out on what I've quoted.

This seems to be the main problem. It seems like most people who are posting really are just posting what they think they have read.

Sometimes it seems like no one is actually reading my posts and just skipping big chunks which is why we are going round in circles sometimes.

So for everyone whos just jumped to this page.

This post explains it the best.
https://www.physicsforums.com/showpos...3&postcount=19
Then read this post
https://www.physicsforums.com/showpos...3&postcount=48
It has a nice big picture.

So, in my big picture...my first drawing. Is that acceptable?

The question is, is IsaacBinary basing his reasoning on the idea that "voltage causes current?"

wbeaty, from all my learning and what I've been taught. I would have to say yes.

You can't have a current without a voltage can you?

When I ask that and people say to me "phase shifts". I say, but the phase shifted current is created out of an overall effect of different components voltages doing different things. But when we plot this on a graph we plot voltage X or voltage Y and then the phase shifted current which is caused by X and Y working together. "Resultant" / "superposition" / "tug of war" how ever you call it. While it may look like on the graph that there could be an instance where there is a current and no voltage. Its just no voltage at X or Y. Thats why we say, WITH RESPECT TO SOURCE VOLAGE. But there are other voltages in the circuit which are changing how it behaves.

So is that understanding wrong?

Im happy to accept I am wrong, that's not the problem but I would like it to be explained the correct way. Just throwing formulas out there does not help one bit.

Im not trying to design a new CPU by throwing my arms about or using anologys and no maths. I can DO the maths and I say that you 200% NEED maths. YOU DO NEED MATHS NO QUESTION ABOUT IT. But maths alone will not tell you what is happening inside.

As for a resistor.

You can think of it that it is a dense material or a material with higher friction so engery is lost by the electrons to get through it.

Actually, sophiecentaur, where has anyone "waved their arms" about? Can you show me?

It seems like most of the frustration is coming because people arnt really reading my posts and question.

Also wbeaty, I've seems a few places here and there about "current drawing" , "loads" etc but I've never come across any learning material about these effects / properties or anything explained in those ways. So maybe I am missing something?

But even if I am missing something, my question still stands.

So can we work together to come up with an explanation / analogy on how and what causes a total phase shift with RESPECT to source voltage.
 
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  • #75
IssacBinary said:
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

You mean if you had an RC circuit you want to know why the Phase is shifted at a certain angle (other than 90 degrees) and how that circuits resistance capacitance values account for a shift in overall phase?... but you want a purely physical explanation of what's happening?... I don't think you will find one.
 
  • #76
This has gone on far too long. We do agree that Maths is a good thing. I can even agree that you need to enter and exit the Maths bit in a valid way (you can prove anything if you don't use the right Maths).

But, when you ask "what's going on inside", I just couldn't start on that question without calling on Maxwell's equations. How, without Maths, would I be able to describe the equivalent of Curl??
The next best thing is at the 'component' level, to describe how current and volts are related for a Capacitor and how current and volts are related in a resistor and then set up the boundary conditions at all the points in the circuit. Why would you Want to do all that without Maths? It's like trying to run with your shoelaces tied together.

We all have little 'private models' in our heads to get us round some of the quirky bits of Science but trying to communicate these highly personal ideas is loaded with the danger of misunderstanding. I have been there with two students, each of whom wants his own model used for the explanation. I may manage to see their two points of view but they never see how the other person's model applies. That's one of the best reasons for using Maths as your common language. It's already been vetted by the scientific World and is, for good reason, used as the means for communication as well as the means for working stuff out.

The answer to the final (repeated) question above is that the simple application of the network equations will tell you the current and volts everywhere in a circuit, however complicated. The non-maths explanation really does fall down if you try to discuss more than a single RC combination - there would be just too many 'parentheses' in the description of what happens to what and why and your audience would be lost / go to sleep during the explanation.

There's a very good reason for all singing from the same hymnbook.
 
  • #77
sophiecentaur, again it seems like you really havnt been reading my posts. Or atleast not fully.

As there several things in my posts, some for you, but just isn't replied to. Instead people are just replying "generalised" posts but no reply to what I might have said.

Im not looking for an explanation which will allow me to go and develop a complex circuit. I am just looking for an overview / general concept of why the phase is shfted at a certain angle which is what foiwater picked up on.

No one seems to have problems with the phsyical models or anologys or explanations of things that are already out there. Capacitors etc. So what is different about what I am asking.

Yes, this thread has gone on very far but I have NOT seen ANYONE try to work with me / together to fix my understanding / come up with an anology / explanation together.
Apart from wbeaty and a few others, All I see is people claiming how it can't be done and how maths is the only thing needed. Just like your students, perhaps you can't accept this can be done / you don't understand yourself?

I ask you, please read my posts fully.
 
  • #78
IssacBinary said:
Yes, this thread has gone on very far but I have NOT seen ANYONE try to work with me / together to fix my understanding / come up with an anology / explanation together.
Apart from wbeaty and a few others, All I see is people claiming how it can't be done and how maths is the only thing needed. Just like your students, perhaps you can't accept this can be done / you don't understand yourself?
.
Perhaps you can take this as a hint that you may be on a hiding to nothing. As was mentioned earlier, by someone, there are all levels of ability on these forums (a real luxury, I'm sure you'll agree) so perhaps this general opinion you are getting back is the answer to your request.
Firstly, the Maths does it so much better and, secondly, no one wants to stick a head above the parapet and give us, publicly, their own pet models, for fear of looking daft. But I am sure we all use them 'in our heads'.
I, for example, always tend to draw (or even re-draw) circuit schematics, when it's practicable with the higher potential bits at the top and the lower (-) bits near the bottom. 'Downhill' and 'Uphill' help me with things. But it can let you down terribly - particularly where electrolytic capacitors in DC feedback loops are concerned.
 
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  • #79
sophiecentaur said:
The bottom line of all this discussion is to ask the question - how many people who design circuits for a living and who make Engineering Systems work do it without Maths and by waving their arms about?

If you don't mind my asking, what's your background? Physics student? Degree? Done any analog design professionally?
 
  • #80
wbeaty said:
The question is, is IsaacBinary basing his reasoning on the idea that "voltage causes current?"

IssacBinary said:
wbeaty, from all my learning and what I've been taught. I would have to say yes.

Then that's another conceptual sticking point. Yes, in resistors, voltage DOES essentially cause current (meaning that e-fields accelerate the resistor's mobile charges.)

It also works the same way for real-world metal conductors. The current in a wire is always caused by a (tiny) voltage applied lengthwise.

But inductors and capacitors are different. In these, the applied voltage doesn't directly cause current. L and C devices ...they're very weird.

IssacBinary said:
You can't have a current without a voltage can you?

Sure you can: a bunch of charges flowing in a ring-shaped conductor are analogous to a flywheel.

If you get this 'flywheel' going at high amperes, then disconnect it from everything, the currents persists for a time. If you used ideal zero-ohm wire, the current will continue forever, a flow without a voltage. If you used actual realworld superconductor, the current will keep going, and only decay over billions of years. It's a kind of electromagnetic inertia, fast moving charges, zero drive volts.


IssacBinary said:
So is that understanding wrong?

Yes.

And also no. In capacitors and inductors, the currents and voltages are divorced from each other. It's easy to produce currents without voltage, and voltages without currents.

It's similar to flywheels: they can keep spinning without any drive force. It's similar to balloons, they can remain pressurized without needing any flow. But still you'd need a brief force to initially accelerate your flywheel up to speed. And still you'd need a brief flow of air in order to inflate your balloon initially. The V and the I are separated in time, and don't occur together.


IssacBinary said:
Also wbeaty, I've seems a few places here and there about "current drawing" , "loads" etc but I've never come across any learning material about these effects / properties or anything explained in those ways. So maybe I am missing something?

Bingo, another sticking point. Resistors are associated with two separate concepts:

1. If you have a constant current in an ideal conductor, and then you cut the conductor and insert a resistor, a voltage drop will appear. You started out with a pure current and no voltage. The resistor opposes the flow and causes the voltage-drop to arise. It's like sticking your hand in a rushing creek and experiencing a force.

2. If you have a constant voltage between two conductors, and then connect a resistor across them, the resistor "draws a current." You started out with a pure voltage and zero current. By adding the resistor, you provided a leakage path between the conductors, causing a current to arise. It's like puncturing a balloon and experiencing an air jet.

Resistors can be leakage paths on constant voltage supplies. Or they can be opposers-of-current in a constant-current power supply. (All these concepts are hidden in intro DC engineering texts on "Thevenin equivalent," and CC and CV supplies.)

Mechanical analogies:

1. if a flywheel is spinning, and you let it rub against your finger, this creates a force which makes the flywheel speed start slowing constantly.

2. If you have a pressurized container, and you drill a small hole in it, this creates a flow which makes the pressure start falling constantly.

In education research, the first one is called "current based reasoning," and most of us learn this version in grade school. "Batteries create current electricity." "Light bulbs consume the current." In physics class, the challenge for the teachers then becomes this: get all the students' minds loose from no. 1 above. They have to be freed up so they can learn "voltage reasoning" as in no. 2.

Your question about phase lies within the domain of no. 2, because capacitors have two functions as well.

1. When inserted into a constant current, a capacitor opposes the current and creates a rising voltage-drop across the capacitor.

But here I think is the key you've been missing:

2. when a capacitor is connected across a voltage-based power supply, it "draws a current." Or said more conventionally: the capacitor's current is proportional to the slope of changing supply voltage.

Suppose you connect a capacitor to a triangle wave voltage generator. When the triangle voltage is smoothly rising, the capacitor draws a perfectly constant current. (The current will be larger for a high-value capacitor.) And, when the triangle voltage is dropping, the capacitor draws a negative current. The upshot: apply a triangle-wave voltage across a capacitor, and the capacitor draws a square wave current from the power supply.

Analogy: if you connect a balloon to a regulated supply of air pressure, then slowly adjust the supply pressure upwards, the balloon will draw a constant air flow as it inflates. Next, adjust the regulated pressure downwards, and the balloon will deflate as it pumps a constant unchanging air flow back into the supply.
 
  • #81
wbeaty said:
If you don't mind my asking, what's your background? Physics student? Degree? Done any analog design professionally?

Physics degree.
24 yrs research engineering with some analogue design and 're-design' / fault finding.
20 yrs teaching GCSE / A level Physics
Fwiw :-)
 
  • #82
@wbeaty
Great last post btw. It shows that the shorthand statements people make are full of misconceptions and often only deal with the specific.
 
  • #83
Wbeaty, you know, you might have just done something right there.
Its late at the moment, 1:30AM, so I am not going to reply very big, ill save that for tomorrow. But I definitely think something is there. Just going to see if I can piece it together and come up with an explanation.

sophiecentaur, again, you seem to be completely ignoring my posts. Also, if your so so qualified as you say you are (im not saying your not) and you see I've got problems in my understanding why arnt you helping me out to fix it and perhaps work together to come up with an explanation?
You wouldn't be just helping me but anyone else who might be looking.

Again, this knowledge I am asking for, along with how a capacitor works and the reactance explanation...of course you don't need to know them to be able to do circuits. If you can use the formulas your good to go. So even if you have 100 years building and design experience you still might not know what's going on.

But I am just asking so when I help explain it to other people and for myself its something to show why there's a lag.
 
  • #84
I think the problem is yours, I'm afraid. Why do you not see the Maths (including graphs, if you like) as giving the best possible description of what's happening?
As I said before, what would be the point in insisting in having an explanation given to you using Latin which is a language which just doesn't have all the necessary words? Maths actually gives you a way of stating relationships in a very concise way. Why do you think it's used so universally? How could you say "Q=CV" in a less complicated way? Why would you want to? It requires that you know the vocabulary, of course, but that goes for the spoken version too.
Perhaps your problem (and I do believe it is a real problem that many people have) is that you believe that somehow there is an ultimate answer to all these questions which can be stated in familiar terms. The fact is that years ago, Scientists realized that words are not enough to describe the processes we see. Since Newton, the Maths has been a basic requirement for understanding things. Why do you not feel that it is adequate. You seem to be saying that it is an optional bolt-on to Science.

If you were describing the motion of an object under the influence of a force, would you insist on not using the basic equations of motion. How could you even start to explain how a simple trajectory is parabolic without involving Maths?

Has anyone else stepped into help you, seeing that I have proved to be so inadequate? Why would that be? I think you may just have to 'join the club' on this one. If you can do the maths then just go along with what it tells you. That's as near to understanding as we can hope for.
 
  • #85
sophiecentaur said:
Physics degree.
24 yrs research engineering with some analogue design and 're-design' / fault finding.
20 yrs teaching GCSE / A level Physics
Fwiw :-)

If teaching, are you on PHYS-L physics teacher forum? How about TAP-L?
 
  • #86
wbeaty said:
If teaching, are you on PHYS-L physics teacher forum? How about TAP-L?

Just this forum aamof. I must do some visiting.
 
  • #87
wbeaty said:
Sure you can: a bunch of charges flowing in a ring-shaped conductor are analogous to a flywheel.

If you get this 'flywheel' going at high amperes, then disconnect it from everything, the currents persists for a time. If you used ideal zero-ohm wire, the current will continue forever, a flow without a voltage. If you used actual realworld superconductor, the current will keep going, and only decay over billions of years. It's a kind of electromagnetic inertia, fast moving charges, zero drive volts.

You don't even need a 'flywheel' to have a current. If you have an excess concentration of charge carriers in one area relative to another area you will have a diffusion current from the high-density area to the low-density area. This can be important in some contexts, most notably in solid-state image sensors.
 
  • #88
I want to put my point.
This seems to be battle of maths/no_maths.
But I ask, what's the difference.
If I start by saying " because, I = C d(Vc)/dt "
You would I scream, its math, I want physical explanation. Actually, I = C d(Vc)/dt is a explanation of physical phenomena, just stated concisely.
You can start like, in capacitor we store charges (electrons). They exert forces on each-other in inverse-square law (columbs law). When we try to push a lot of them into a metal plates (capacitor) they try to oppose. If we connect them to a source in series with a resistor (which acts like a bla bla...) then the electrons oppose ...
Bla bla bla... Due to the nature of electrons, capacitor seems to follow a strange behaviour, which can be accurately modeled by, I = C d(Vc)/dt.

So, instead of speaking the long paragraph each time, we use the mathmatical formula. The funny thing is, not everyone knows or understands, the long paragraph but only the formula. Just like we accept the columbs law (Have you tested this theory? I haven't) as a fact that can be tested by experiment, Some people like myself, accept, I = C d(Vc)/dt as another fact that can be tested. Ofcouse, you don't need to accept both fact, one can be logically derived from other, but it simplifies my life and let's me make machines that do my job.
 
  • #89
@I am learning
Well put. The suggestion in a previous post that you can look upon a circuit as a flywheel would never have been made if Maths had been used. Maths involves actual numbers and would have revealed the sort of value for the angular momentum involved with 1/4000 of the mass of the wire and speeds of a few mm/second being involved. A Flywheel??
 
  • #90
I_am_learning said:
I want to put my point.
This seems to be battle of maths/no_maths.
But I ask, what's the difference.
If I start by saying " because, I = C d(Vc)/dt "
You would I scream, its math, I want physical explanation. Actually, I = C d(Vc)/dt is a explanation of physical phenomena, just stated concisely.
You can start like, in capacitor we store charges (electrons). They exert forces on each-other in inverse-square law (columbs law). When we try to push a lot of them into a metal plates (capacitor) they try to oppose. If we connect them to a source in series with a resistor (which acts like a bla bla...) then the electrons oppose ...
Bla bla bla... Due to the nature of electrons, capacitor seems to follow a strange behaviour, which can be accurately modeled by, I = C d(Vc)/dt.

So, instead of speaking the long paragraph each time, we use the mathmatical formula. The funny thing is, not everyone knows or understands, the long paragraph but only the formula. Just like we accept the columbs law (Have you tested this theory? I haven't) as a fact that can be tested by experiment, Some people like myself, accept, I = C d(Vc)/dt as another fact that can be tested. Ofcouse, you don't need to accept both fact, one can be logically derived from other, but it simplifies my life and let's me make machines that do my job.

IM NOT SAYING we can work out everything without maths. NO. OF COURSE you need maths.

So your telling me if you told someone

I = C d(Vc)/dt

they will be able to see what it means and just come up with the long paragraph explanation which you just told me? about the electrons moving, more there are the more push is needed etc..

I sure don't know anyone that does...

I can do the maths, I can get the end result and know what it means.

But I want a LONG PARAGRAPH that generally explains what is causing the OVERALL phase shift in the circuit: total impedance phase.

So...can you tell me?
 

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