Unraveling the Mystery of Phase Differences in Passive Circuits

[IssacBinary]

Hey DailyDose,

Thanks for your input. I am glade someone sees things the way I do.

It seems like you might be thinking I am stuck on what phase means as a definition?
I know it means the time difference / difference between cycles, between the same points on different waves.

But what I am actually asking is what is the mechanics behind the effect that is creating OVERALL phase in a circuit (with a capacitor and resistor). Which is the phase part when we work out total impedance of a circuit.

NOT why there is a phase of 90 degrees associated with a capacitor as its own unit. (Voltage lags current 90 degrees across capacitor)

Did you see my post #19 DailyDose?
https://www.physicsforums.com/showpost.php?p=3377063&postcount=19

That should help you see what I am after?.
Let me know if you have any questions and if I've made sense. haha

Thanks

 

[sophiecentaur]

Im not looking for an analogy to answer my question. However they might help get there.

@sophiecentaur
I think you think I am looking for an analogy, and this is where your saying I can't find one because everyone might have their own different ones...and that even if it gets them through it, it might be wrong.


But ultimately I am just looking for a basic explanation. Not an analogy but also something that doesn't rely on maths phrases.

Hopefully that might help people see what I am after a bit more.

Yes sorry, when I say it gets charged less when talking about AC I mean that it has a less max voltage.

I was not addressing you in that post. I was addressing the analogy that Iamlearning produced and suggested a way that could make it more meaningful. (Not necessarily for your benefit.)

What actual terms are 'allowed' in your "basic explanation"? Would the explanation need to verbalise time derivatives and complex numbers or would those, totally mathematical ideas be acceptable.
My problem with your request is that you seem to be happy with the use of some totally naive ideas of electron flow and 'forces' to explain aspects of electricity that are far more sophisticated than that. How far would you expect to get with a proper 'understanding' if you are prepared to build your structure on such dodgy ground? You are being very selective in which analogies you will and won't accept, bearing in mind that all the pictures you have been using so far are, as we all know, analogies.

 

[Studiot]

Throughout this thread you have kept referring to the capacitor "in opposition" to the source and indeed in post#48 produced some erroneous diagrams to suggest that a capacitor that has previously been charged to 2 volts and is then connected to a 10 volt source will do something other than be charged to 10 volts.

Until you abandon this wrong thinking no progress can be made.

 

[IssacBinary]

Ive just checked that picture and I realized I made a big mistake. The last battery was meant to be an AC source. (thats why there's an AC voltage graph underneath it)

The 2V is the max voltage the cap can get with that X frequency. Basically to represent a high frequency so the cap doesn't have enough time to charge and there for has a smaller max voltage across it.

Im just in the process of writing a new explanation which I think is it / very close. Hold tight!

 

[sophiecentaur]

Of course, you realize that the Capacitor never actually reaches the same voltage of the supply - even with DC. This is because the DC must have been switched on at some time and the exponential voltage change never actually gets you there ( whatever the RC time constant). You have to have a finite value of resistor in order to analyse the circuit or 1. the Inductance of the connecting wires (however short) will be significant and produce a continuously oscillating voltage after the switch is thrown and/or 2. the em radiation from the circuit needs to be taken into account and introduced as a damping factor on the LC circuit by virtue of the radiation resistance of the structure.

 

[Studiot]

SC don't you think that's rather overcomplicated at this stage?

 

[I_am_learning]

I am learning.
That diagram of a mechanical circuit is not correct if your crank wheel is to be a voltage source. The 'friction patd' you have drawn appears in an electrical circuit as a resistor in parallel with the generator an has no effect. The 'correct' place to put the frictional component would, I think, have to be in series with the push rod. Something like a piston with holes in a hydraulic cylinder (with no mass, of course) perhaps.

Analogies are full of pitfalls, alas.

Yeah The crankshaft isn't perfect. I realized that. And I have already mentioned it. (Just above your post in Caution note)
As Long as you accept sinusoidal force is being applied at the tip of the spring, rest of the analogy is perfect. Namely the two differential equations for the system are
Vsin(wt) = R dq/dt + q/c (electrical)
Fsin(wt) = B dx/dt + x*K. (mechanical)

And properly made analogies don't have pitfall and may actually help us understand things.
@IsacBinary why are you running away from understanding this analogy? To show sophiecentaur that you are not onto analogies. Ok, fine you may not be onto it. But You have to demonstrate that you atleast understand the analogy. You didn't fully reply to my previous post where I corrected your 'wrong' interpretation of the analogy. Can you demonstrate that you can now correctly interpret it?

 

[sophiecentaur]

SC don't you think that's rather overcomplicated at this stage?

And @I_am_learning
Yes, you both have a point there but, to examine what's happening and to come to a valid conclusion, you need a loss mechanism somewhere and it needs to be in the right 'place'. The fact is that the friction mechanism in that mechanical diagram will have no effect on the displacement of the spring, which is not a parallel of the electrical model, in which the resistor will have an effect on the charge on the capacitor. There is nothing wrong with the two equations, given for the systems but they are actually describing two very different setups. In the electrical model, the components affect each other whilst, in the mechanical system, they do not. To my mind, when trying to make an analogy, that is a very relevant difference and could compromise understanding. (For instance, in the legend below the diagram, there is reference to an "applied sinusoidal force' when it is really an "applied sinusoidal displacement". If the crank were replaced by a solenoid driven with AC (a sinusoidal force), the analogy could be more appropriate, perhaps. I_am_learning won't mind my pointing out something like that, I am sure - it all adds to the general level of understanding.

 

[I_am_learning]

If the crank were replaced by a solenoid driven with AC (a sinusoidal force), the analogy could be more appropriate, perhaps. I_am_learning won't mind my pointing out something like that, I am sure - it all adds to the general level of understanding.

Thanks. That would be perfect. Actually, I couldn't come-up with any mechanism that could produce sinusoidal force hence the crank.
But I am still not clear why you are not satisfied with the Resister modelling. Pherhaps you are misguided by the crank setup (that would always produce the same maximum displacement)
Lets replace it with the solenoid setup. Now, the displacement is dependent upon friction.
Actually, I am not comparing the two systems based on what mechanically would happen, but
since the Differential equation are perfectly identical, I was assuming it to make perfect analogy.

 

[sophiecentaur]

I think what is wrong with your original setup is that the drive is NOT a sinusoidal Force - it's a sinusoidal displacement. I now think the problem is that your actual equation does, in fact, not describe your mechanical model. The equation is fine for 'our' modified model, using a solenoid or equivalent. The displacement of the spring (aka capacitor volts) would then depend on the value of the resistor - which is what you want.

An approximation could be to use a crank and a very long, weak spring (=a dodgy battery )

 

[I_am_learning]

Yeah, I already accept several times, the crank isn't the correct model. That would be sinusoidal velocity source equivalent to sinusoidal current source. Solenoid is great.
Thanks.

 

[IssacBinary]

@I_am_learning
Sorry I was actually writing a reply and then got a bit distracted by some other posts. But I am not trying to run away from it.

Sinusoidal force is fine.

So as it turns the force goes up and down. It has to overcome the friction, and anything left is transferred into the spring.

The force being produced by the spring is the voltage across the capacitor.

The force from the spring will keep increasing until it is equal to the source force. Depending on how much friction is there means it will either be close to the source max force or not...high friction means the source force has to use a lot more energy to overcome the friction so less will be left to transfer into the spring.

When they equal there will be no movement of the spring tip. i.e No current. EVEN THOUGH the source may not be 0 Newtons yet but its still in a force producing state but its being canceled out by the push back of the spring. *

When the source is less than what's in the spring, the spring starts to win and push (discharging capcitor). Current is now on its second part of the cycle, negative. Even though there could still be a positive force at the source. *

Once the source has also changed directions both forces combine to create a larger current than if the spring wasnt there (only happens once the spring has been energised for the first time.)

Same with the capacitor. We now have the charge stored in the capacitor along with the current generated from the AC source voltage. and when the capacitor starts to discharge the current from there and source combine to create a large current than if the capacitor wasnt there.

That makes sense to me, and its always something I've thought about. Using a few circuit simulation programmes it also confirms it. If it take out the capacitor the current is less in the circuit (after the initial charging). However what stumps me here is the maths.
We use total imedance to work out the current in the circuit when there's a capacitor present. But that seems to indicate LESS current than if the capacitor wasnt there.* This is what is causing the overall phase shift which is what my question has been.p.s I realize we don't say charging a capacitor in AC, so what term is used to describe a capacitor gathering charge and creating a voltage across it in AC circuits?

 

[I_am_learning]

I often find it easier to analyze things, when I push things to extremites. Suppose, there is very little ( 0) friction. Then, we will have only a sinusoidal force on a spring. Maximum velocity (current) occurs when the spring isn't pushing (0 Voltage) and minimum velocity occurs when the spring is pushed to its limit (max Voltage). Be aware that the applied force is equal to the force by spring, at all times.So, Velocity maximum occurs when the applied force is at 0.

Lets push into the other extrimity. Very feeble spring (almost no spring) and a very high resistance. In this case the applied force is at all times equal to the reaction force developed by the friction (resister). However, in this case the reaction force is directly proportional to velocity (current). So, Applied Force maximum and Velocity Maximum Coincide.

When both the resistance and Capacitor are of comparable magnitude, the two forces created by them add up to be equal to the source Force. The velocity for both of them will be same.
One(resistance) will create maximum force when velocity is maximum . One (capacitor) will create maximum force when velocity is 0. But the two forces add. So, the net force (which is equivalent to source force) is maximum not when Velocity is 0, not when velocity is max but in between. The in-between point depends upon how strong the friction and the spring is.

Feel free to ask where you don't get me.

 

[IssacBinary]

haha that's how I like to look at things also.

Theres nothing I don't really "get" in your last post.

Would it be ok if you replayed to my post and comment on what I've said? that way it will help tie the bits together.

But your post seems to be pretty fine.

 

[I_am_learning]

In your previous post, I don't find you mentioning about friction force being proportional to velocity. I hope You aren't missing this point. You appear to be talking mostly only about the applied force and spring, and appear to take the role of resistance as only to magnify or diminish the magnitude.

 

[IssacBinary]

Im not to sure what exactly you mean / the point I am missing.

But the resistance IS NOT only to change the magnitude. It effects the phase also.
Higher the friction the less max force is generated by the spring and for the max force in the spring to equal the source force it would happen later on in the cycle rather than sooner.

This will make 0 current occur closer to when the source force is also at zero. So high resistance, little phase shift.

Thus higher the resistance the less phase shift between current and source voltage.

A very low resistance alows the capacitor to charge up to a high max voltage which would mean they would equal sooner than before. It would reach max voltage just after the source reached max voltage. This will end up creating almost 90 degree shift in the source voltage and current.

So lower resistance higher phase shift.

Which is what the * are explaining in the previous post.

I do think I've got it actually. Remember I am looking for an explanation that just describes what's happening to cause the effect. Not something that predicts exact numbers or anything, more on just the relationships.

But I am still a bit stuck on the last thing I said in my previous post. About the higher current and the charging term

 

[I_am_learning]

Im not to sure what exactly you mean / the point I am missing.

But the resistance IS NOT only to change the magnitude. It effects the phase also.

Nice that you understand it.

I do think I've got it actually.

Nice to hear that.

But I am still a bit stuck on the last thing I said in my previous post. About the higher current and the charging term

I don't think there is another term. When you are looking at the fraction of cycle, its fine to use the term 'charging'.

 

[IssacBinary]

haha you sound a bit sarcastic there.

So are you happy with that explanation that I gave?

And lastly, what about the higher current calculation?

 

[sophiecentaur]

That makes sense to me, and its always something I've thought about. Using a few circuit simulation programmes it also confirms it. If it take out the capacitor the current is less in the circuit (after the initial charging). However what stumps me here is the maths.
We use total imedance to work out the current in the circuit when there's a capacitor present. But that seems to indicate LESS current than if the capacitor wasnt there.

I'm not sure what this means. Do you mean replace the Capacitor with a short circuit or with an open circuit?
The Magnitude of the Impedance if there is a C in series with the R will always be higher than if the R is on its own. So would you not expect the Current to be less?
I=V/Z gives both magnitude and phase of the current just like I=V/R for resistive circuits.

 

[IssacBinary]

Completely forget what I just said. I tried to make it happen on the programme but now its not doing it and is fitting the equations. ha. I have NO idea how it happened last night.

sophiecentaur, could I have your opinion on my explanation in #162 and #166.

To me it seems all correct and if there's nothing horribly wrong ill write up a final explanation to hopefully answer my own question.

 

[I_am_learning]

Ahh! I got your description now. Actually, at the first reading I couldn't grasp what you were trying to say so I simply ignored it. After your repeated mentioning of higher current, I re-read it.
You had a serious mistake. The current (velocity) can't be greater than what would flow without the capacitor (spring).

In #162 You are all fine upto saying that "Once the source has also changed directions both forces combine". But Combining both force won't give much large force, because, the applied force has just done the zero crossing, its magnitude is small. By the time, it reaches its peak, the force in the spring would already have decreased and even reversed. So, there is no such point in between where there combined action create current more than that would flow without spring.

Actually, I had never analyzed this circuit this far. Fun to do it.

 

[IssacBinary]

Ahh! I got your description now.

Your talking about the "higher current" than without the capacitor part?

Yeh I realized it was wrong. I have no idea what I saw on the programme last night! ha.

But yeh I see your point also.

Actually if using a square wave then it does reinforce, so it must have been that that I was looking at last night and didn't realize!

I_am_learning, could you give me just your last thoughts on #162 and #166. Just to make sure we are on the same level now.

When I get back in tonight ill rewrite it all up into a nice package, and as long as its all correct it will be what I've been looking for :)

Thanks again everyone.

 

[sophiecentaur]

sophiecentaur, could I have your opinion on my explanation in #162 and #166.

To me it seems all correct and if there's nothing horribly wrong ill write up a final explanation to hopefully answer my own question.

My opinion is that it just goes to demonstrate just how much verbiage is needed in order to describe what a single line of Maths tells the initiated reader. If the Maths is not telling you the message then I think it's up to you to get so familiar with it that its messages come through loud and clear.
You use phrases like "it has to overcome the friction" - as if it sticks until there's enough force to shift it. That may happen with jam jar lids but not in ideal mechanical models which have friction and not stiction. That sort of hiccup in an already heavy-going explanation can reduce the value of the whole thing. You are using your own, personal, vocabulary which may be OK inside your head but it just gets in the way of communication with other people.

I was almost asleep before I got to the end, I'm afraid. I just kept thinking to myself "If he wants to say that, why not just state the Maths and be done with it?" What possible advantage is there in piling mental picture on mental picture just to make a point of avoiding the succinct and unconfusing terms of Mathematics? This is nothing to do with understanding. It's to do with the relationships between variables. Would you say that a Graph is not a good way of describing a process? Would you prefer to use the words "it goes up then it goes down, but not so far this time blah blah"? That is precisely what your great long paragraphs are doing. Springs that "want to do" things have no place in getting to a true, communicable, understanding of an idea.

I admire your true grit at sticking with this and I see that you have an urge to get somewhere but you seem to be constantly shooting yourself in the foot rather than using the tools available to you. I keep trying to get the message across There may not be an answer that will satisfy your present requirement: You may be the one who needs to change - not the rest of us / the World.

 

[sophiecentaur]

Actually if using a square wave then it does reinforce, so it must have been that that I was looking at last night and didn't realize!

Yes but you are changing the goal posts here. If you look at all the indiviaual frequency components of the square wave, none of them increases in amplitude. It is just that their SUM may be higher than the max of the square wave because their relative phases have changed. The Impedance varies as the frequency varies. One thing at a time, please!

 

[I_am_learning]

I actually edited my #171. The un-edited version had error. The voltages actually re-enforce just like you mentioned in #162.

 

[I_am_learning]

IssacBinary, you are indeed very strange. I myself, avoid trying to visuallize and follow step by step instants on the cycle. I understand it like this: "when I make this and this arrangements, and apply sinusoidal force here, some crazy things must happen". I then use maths to find out what will happen (instead of trying to analyze like you). After the solution is found, I try to visualize what the solution look like. I find it plausible and say, 'That looks ok. let's move on'.
However, I was at beginning, I was also like you, trying to gain insights by analyzing every moment. But given so many things to learn and so many arrangements and complexities we need to deal with, its not always possible.
For eg, if I draw out some another similar similar circuit with few more capacitors and inductors, and if you try to visualize the oscillation involved there in a way you are trying to do here, then you may burst your brain. :)

 

[Bassalisk]

I got a magic answer, that i personally learned over the past year. Its universal.

"You don't have to visualize everything to understand it". Phase is one of those things. If you can use it calculations, what's the point? Math is always there to back-up everything.

 

[NascentOxygen]

I got a magic answer, that i personally learned over the past year. Its universal.

"You don't have to visualize everything to understand it".

If you say that works for you, then I'll take your word for it. But I sure would not recommend that others subscribe to that notion.

Phase is one of those things.

Phase is so easy to visualise, and to illustrate, that I can't see why anyone would want to
evade doing so. It can only help understanding. Visualisation takes the mystery out of many concepts, and aids design and troubleshooting.

Wasn't it Tesla, the greatest electrical engineer ever, who designed his motor in his mind. When someone asked would he be building one so he could test it, he replied there was no need, he had already run the tests on it in his mind.

If you can use it calculations, what's the point? Math is always there to back-up everything.

Maths is not a whitewash for a meagre understanding.

 

[Bassalisk]

If you say that works for you, then I'll take your word for it. But I sure would not recommend that others subscribe to that notion.
Phase is so easy to visualise, and to illustrate, that I can't see why anyone would want to
evade doing so. It can only help understanding. Visualisation takes the mystery out of many concepts, and aids design and troubleshooting.

Wasn't it Tesla, the greatest electrical engineer ever, who designed his motor in his mind. When someone asked would he be building one so he could test it, he replied there was no need, he had already run the tests on it in his mind. Maths is not a whitewash for a meagre understanding.

Understanding mathematically what is happening can be enough for me. Yes Tesla did run tests in his mind, but in my opinion he was an innovator not a scientist, he didn't bother too much with formulas. Maxwell was a scientist and he had greater power of understanding by having very good math. This is solely my opinion and I am first year EE. This is my comprehension of my current knowledge of EE.

I am only for understanding everything physically. But I can't sometimes and math gives me good bedding.

 

[f95toli]

Phase is so easy to visualise, and to illustrate, that I can't see why anyone would want to
evade doing so.

Phase is not always easy to visualize. I did my PhD working on current phase relationships in high-Tc superconductors. In these materials the phase shift depends on the direction the current in flowing with respect to the crystal axes (due to the d-wave symmetry of the pairing wavefunction); the microscopic theory for this is very complicated. Moreover, one of the things I measured was the quantum mechanical tunnelling of the phase. At low enough temperatures the phase of a electrical circuit can become quantized, meaning it can go from one value to another via tunnelling (phase is actually the conjugate variable to charge); this is once again a good demonstration that phase is a much "deeper" concept than most people realize (meaning there is more to phase than just time-differences if that is what you were referring to).

Hence, yes there are situations where one CAN "visualize" the phase. But this is not true in general, and relying to much on "visual" pictures and analogies for phase and similar things can become a serious problem later on when you study more advanced physics (very few things in for example quantum mechanics can be visualized, or even understood in the conventional meaning of the word). It is therefore important that you get used to understanding things at an "abstract" level early on, you need to be able to "think" math.

 

[Studiot]

Phase is not always easy to visualize....

Funny that, I was going to reply with a similar comment but stopped for a cup of tea and there was your post when I came back.

I was just starting to prepare a qm response for another thread and saw and saw this.

If your function is say

\Psi = {\Psi _0}\exp \left( {\frac{{i(xp - Et)}}{\hbar }} \right)

I definitely find phase less than easy to visualise directly.

go well

 

[sophiecentaur]

Wasn't it Tesla, the greatest electrical engineer ever, who designed his motor in his mind. When someone asked would he be building one so he could test it, he replied there was no need, he had already run the tests on it in his mind.

I have to take issue with that (tongue-in-cheek?) description of good old Nicola. An Engineer is someone who actually implements a viable version of what an Inventor may produce in the form of a prototype or a description. He was a great Character, no doubt but the rest is far too much of a myth for me to take seriously. Distance lends enchantment, I think.

 

[NascentOxygen]

Phase is not always easy to visualize.

Phase is easy to visualize in the topic of this thread, viz., the phase shift in a 1st order passive circuit. We are not even onto 2nd order circuits, yet.

The distraction of fluid friction and crank shafts was, I thought, bad enough. Now we have quantum physics wanting to poke its nose in. No wonder the OP is still apprehensive about his shaky understanding after nearly 100 posts on (and off) the topic.

If he can't grasp the simplicities of phase differences in passive circuits, he will stand no hope when he progresses to more complex circuits.

The challenge is not to complicate the scenario to such an extent that the learner has no chance of understanding it. That's easily done. (As you very capably demonstrated)

The OPs best interests are served by placing yourself where he is, and progressing in measured steps from there. Phase shift is easy to visualize, and OP has been able to do that right from the start. The whole thread (yes, there is supposed to be a common thread somewhere in here) came about because he wants to know how, in an R-C circuit, a phase intermediate between 0 and Pi/4 comes about. Quantum phenomena, as interesting a distraction as they may be, have nothing to do with it.

 

[NascentOxygen]

I have to take issue with that (tongue-in-cheek?) description of good old Nicola. An Engineer is someone who actually implements a viable version of what an Inventor may produce in the form of a prototype or a description. He was a great Character, no doubt but the rest is far too much of a myth for me to take seriously. Distance lends enchantment, I think.

Tesla does have a reputation of being a bit of a showman, but I wasn't referring to that. He was both inventor and engineer. Holding a patent on the invention of the induction motor firmly earns him his place in the halls of engineering, quite apart from all his other works. While he is mostly remembered for his work with alternating current, but wasn't it Tesla who discovered a way to generate ball electricity--and store it? No one has been able to replicate that feat. Eccentric, sure, but still with all the traits of the quintessential engineer in my books.

The only black mark I care to place against Nikola Tesla is that he took the secrets of some of his inventions to his grave. But given the way he was not appreciated in his time, who can blame him?

 

[f95toli]

Phase is easy to visualize in the topic of this thread, viz., the phase shift in a 1st order passive circuit. We are not even onto 2nd order circuits, yet.

So what? The question was "Physically, what is phase?". And the OP has already stated that he/she does not accept a mathematical description. Hence, one must then assume that what is needed is some sort of physical model of what is "really" going on. What I am saying that the concept of phase is actually quite complicated. Note that in all of the examples I mentioned above I was referring to real electrical circuits (chips), circuits that are modeled using LCR circuits and where the phase is measured using oscilloscopes etc.

The only reason I brought up superconductors is that it is a nice example; there are many more "mundane" examples where dealing with phase shifts can become even more complex, such as ferrite components (used in high frequency circuits). Even if there was a simple explanation for what is being asked, I don't think I would necessarily give it; simply because that would make it even more confusing when dealing with more complex problems (even in fairly trivial cases such as understanding the physics of an inductor or non-linear components) .

If he can't grasp the simplicities of phase differences in passive circuits, he will stand no hope when he progresses to more complex circuits.

Agreed,

The OPs best interests are served by placing yourself where he is, and progressing in measured steps from there. Phase shift is easy to visualize, and OP has been able to do that right from the start. The whole thread (yes, there is supposed to be a common thread somewhere in here) came about because he wants to know how, in an R-C circuit, a phase intermediate between 0 and Pi/4 comes about. Quantum phenomena, as interesting a distraction as they may be, have nothing to do with it.

I have been where the OP is. But I got over it.
The problem is -as we keep coming back to- is that the kind of non-mathematical "understanding" that the OP is asking for does not necessarily exist; sooner of later (and the sooner the better) one reaches a point where one has to learn to "think" math, where understanding the model and the math means that one has understood the problem fully.

 

[DrClapeyron]

I have always thought about phase as being a periodic change in voltage, and thought about electrical components in a circuits as a way to produce a voltage pattern to send signals.

I think of AC current like this: for the standard American house hold outlet you get 120v of electricity 60 times every second or 60 Hz. Extending that to a three phase power distribution system, you have three phases, one on each conductor, which connect to a motor or single transformer that when they arrive act like one phase. Almost as if they were staggered like Olympic sprinter starting points, where you have to take into account a runners distance from the inside of the track.

Therefore I have always thought of phase as a package of varying voltages. I have no idea if this is correct but I can not help being curious.

 

[NascentOxygen]

Generally speaking, a working concept of any phenomenon need be no more complex than is necessary to adequately serve your needs.

I think of AC current like this: for the standard American house hold outlet you get 120v of electricity 60 times every second or 60 Hz.

There is nothing wrong with what you write. But it would be even more correct to say that you get up to 169v of electricity so many times every second. Remember that 120v is the RMS value of the sinusoid. Your 120v supply smoothly swings from -170v to +170v every cycle. (120 x sqrt 2 = 169.7)

While I can see why you wrote "60 times every second" you could equally have said 240 times every second.

 

[NascentOxygen]

So what? The question was "Physically, what is phase?".

No. That's the subject header. For the question you have to read the message that comes under that header. (I sharn't repeat it here, because in his second post, OP further defines and refines his question.)

And the OP has already stated that he/she does not accept a mathematical description.

Sorry?? "Does not accept" you say?

Let's take a look...

I understand them mathematically

Difficult to see any refusal of a mathematical representation there!

What I am saying that the concept of phase is actually quite complicated.

The concept of phase difference in a linear passive circuit (which is what is under discussion here) is only as complicated as you wish to make it.

I fear that the OP has long ago abandoned reading this derailed thread. But just in case IssacBinary is still soldiering on (in the vain hope of a modicum of enlightenment), I hope that somewhere in this miasma you have been moved a little farther along the path to understanding the genesis of phase differences in a first order R-C system. I believe I can, belatedly, see exactly what you were hoping to have explained. But this thread has staggered on for too long, and I'll leave it until the question arises at another time, to write around the explanation sought.