Why does current lag behind voltage in inductor?

[sophiecentaur]

I've seen that this question has been asked but never answered because guy was silent on formulas.

I can say that i am familiar with formulas, and i know how to derive the equation for current, and that II/2 lag, but here is the thing... Why? i know that formulas say so... But can someone please try to explain this to me in more touchable and intuitive way ?


Thanks

Science has always tried to arrive at descriptions of processes which do not rely on the "intuitive" because intuition potentially leads you into unfounded conclusion. Analogies are great but the greatest analogy is surely Maths. If, as you say, you are familiar with the formulae and what is implied by expressions like "time derivative" then you won't improve much on that. A lot of forum discussions involve stretching analogies further and further to fit something which Maths describes pretty well. It's as if people want the understanding without all the real sweat that is necessary.
Don't put the maths aside. Hang on to it- it's your friend.

 

[Bassalisk]

Math rox, I have a pretty good math. But in my life, physics > math always. Why?

Because math is too abstract, its all raw numbers. I don't think scientists came up with an answer purely by shooting formulas.

All i say is that some equations must have a thought background.

 

[sophiecentaur]

No no. Maths is not just "raw numbers". A sub set of Maths which we call Arithmetic is Numbers but the Greater Maths is about describing relationships between quantities and describes these relationships like no ordinary sentence or arm waving can. If you really want to get into Science then there's no alternative, I'm afraid. Everything else can only be second best. Naturally, you have to pick the right symbols and operations to describe a scientific idea. But that is just part of the deal. I can't think of a single advancement made in Physics in the last 100 years that didn't involve some Maths. Why do you think that is?

 

[Bassalisk]

No no. Maths is not just "raw numbers". A sub set of Maths which we call Arithmetic is Numbers but the Greater Maths is about describing relationships between quantities and describes these relationships like no ordinary sentence or arm waving can. If you really want to get into Science then there's no alternative, I'm afraid. Everything else can only be second best. Naturally, you have to pick the right symbols and operations to describe a scientific idea. But that is just part of the deal. I can't think of a single advancement made in Physics in the last 100 years that didn't involve some Maths. Why do you think that is?

True

 

[sophiecentaur]

And, to continue my rant (indulge an old man), the very fact that we can use maths to describe these relationships, from setting up descriptions of processes in mathematical models, means that we can see parallels in the many areas of Science. This is where the no-Maths enthusiast may pick up and run with an analogy but getting the final conclusion wrong because there wasn't exact equivalence between the two models (which the Maths would have shown up). It all becomes just an 'interesting' set of instances which are fun to talk about in the pub - but that's all.

 

[Pagedown]

I have a question related :

Why capacitors blocks DC signal while passes AC signal? I know the formula Xc=1/jwC. If frequency is 0 then the impedance is inf. But why in theory?

Does inductors block DC current too?

 

[sophiecentaur]

The reason that a capacity "blocks" DC is that charge will flow through it (i.e. it will charge up) until it is fully charged, after which, no more current can flow. How soon it reaches this point depends upon the series resistance of the circuit. This even happens when a switch os opened; a tiny current will flow until the two contacts of the switch have miniscule charges on each (but only for a nanosecond or less) and the total circuit voltage is dropped across the contacts.
Bearing in mind that an inductor consists of an unbroken length of wire, it can hardly "block" DC. What will happen is that, eventually, the voltage drop across it will go to zero (as the Magnetic field reaches its final value and stops changing).

 

[cabraham]

When you first started to study electricity they threw u gradients and divergences and u understood it all instantaneously?

Being pushed and pull, of course we do not mean that literally. To push and pull u need a force, which u do not have in inductor. Key word is analogy my friend.

I have no beef w/ "analogies" but sometimes bad habits can be developed using analogies. When I had gradients & divergences thrown in my face, sure I struggled, & it took time to understand them, but I'm much better off for it now. Had I been presented w/ "push, pull, etc.", I may have developed misconceptions that would have taken years to erase, if ever.

I've noticed that the "pushing/pulling current" heresy is very hard to get people to let go of, so I avoid it 24/7. Although the laws of physics & the associated math are tough at 1st glance, a beginner is better off struggling for a while. Once the concept is understood, they can go on to more advanced viewpoints & not struggle.

FWIW, I use the term "current drawn". I'll say that this motor draws 30 amps at start up & 5 amps steady state. As long as we understand that this is colloquial & not literal, all is well.

A person who sees current as being "pushed" seldom gives up such heresy. They will not progress to the next level. When semiconductor physics is discussed, or energy bands, conduction in semi & metals, Faraday's induction law, etc., that darn "pushing/pulling" heresy keeps rearing its ugly head, & efforts to dispel it are usually not successful.

Trying to explain electrical concepts w/ fluids, and/or "pushing/pulling something" etc., results in bad habits & misconceptions being developed. These myths hinder the student from advancing to deeper understanding of things.

I would recommend, based on my 1/3 century of EE practice, to learn things from peer reviewed texts. If the math is too advanced, there are books that cover the math as well. To really understand circuits at the micro level requires the understanding of e/m fields. But to learn e/m fields, one must learn the math. The concept of vectors, phasors, integrals including line, surface, & volume integrals, ordinary, total, & partial derivatives, as well as curl, divergence, gradient, & Laplacian operators, is needed to fully appreciate what is involved.

Having said that, if time does not permit such effort, I concede that an analogy could be helpful. But I urge all to not push the analogy too far, & do not view the analogy as an equivalent to the e/m problem under scrutiny. View the analogy as a means of covering something complicated by invoking something we understand from everyday life. The analogy is not the law. Please do not invoke simplified analogies as if they were law, since they are not law.

Otherwise, analogies can indeed be helpful. I hope I've made my point.

Claude

 

[Bassalisk]

I have no beef w/ "analogies" but sometimes bad habits can be developed using analogies. When I had gradients & divergences thrown in my face, sure I struggled, & it took time to understand them, but I'm much better off for it now. Had I been presented w/ "push, pull, etc.", I may have developed misconceptions that would have taken years to erase, if ever.

I've noticed that the "pushing/pulling current" heresy is very hard to get people to let go of, so I avoid it 24/7. Although the laws of physics & the associated math are tough at 1st glance, a beginner is better off struggling for a while. Once the concept is understood, they can go on to more advanced viewpoints & not struggle.

FWIW, I use the term "current drawn". I'll say that this motor draws 30 amps at start up & 5 amps steady state. As long as we understand that this is colloquial & not literal, all is well.

A person who sees current as being "pushed" seldom gives up such heresy. They will not progress to the next level. When semiconductor physics is discussed, or energy bands, conduction in semi & metals, Faraday's induction law, etc., that darn "pushing/pulling" heresy keeps rearing its ugly head, & efforts to dispel it are usually not successful.

Trying to explain electrical concepts w/ fluids, and/or "pushing/pulling something" etc., results in bad habits & misconceptions being developed. These myths hinder the student from advancing to deeper understanding of things.

I would recommend, based on my 1/3 century of EE practice, to learn things from peer reviewed texts. If the math is too advanced, there are books that cover the math as well. To really understand circuits at the micro level requires the understanding of e/m fields. But to learn e/m fields, one must learn the math. The concept of vectors, phasors, integrals including line, surface, & volume integrals, ordinary, total, & partial derivatives, as well as curl, divergence, gradient, & Laplacian operators, is needed to fully appreciate what is involved.

Having said that, if time does not permit such effort, I concede that an analogy could be helpful. But I urge all to not push the analogy too far, & do not view the analogy as an equivalent to the e/m problem under scrutiny. View the analogy as a means of covering something complicated by invoking something we understand from everyday life. The analogy is not the law. Please do not invoke simplified analogies as if they were law, since they are not law.

Otherwise, analogies can indeed be helpful. I hope I've made my point.

Claude

I agree, i must emphasize also that i am first year at EE and i simply do not have the tools to understand all immediately. U also must know that I also have an urge for deeper understanding, but u must take steps. U start with analogies and end up with most deepest thoughts.

I remember my first view of orbits in atom, quantum numbers, how our teachers described it. Now, totally different view.


Sometimes math equations can be very hard to understand immediately.

But all in all, I get what you are saying.

Thanks

 

[Bassalisk]

I would suggest that the reason current lags voltage in an inductor has to do most w/ energy. An ideal inductor would possesses no capacitance or resistance. Changing the voltage on an inductor requires no work. But changing the current requires work, since inductor energy is W= (L*I^2)/2. It takes time for energy to change, the rate of said change is power. To change current instantly would require changing energy instantly, which is infinite power. The discussion would then be theological, not physical.

Since time is needed for an energy change, time is needed for a current change in an inductor, but not for a voltage change since no work is done. A capacitor is the complement. The current can change quickly since the energy is not changing. But a capacitor cannot have its voltage changed instantly because that would require an instant energy change & infinite power.

Claude

Can u explain this approach more? Why u don't energy to change voltage but energy to change current.

I am confused about this in AC. If you change the potentials, wouldn't you increase current as well?

 

[haleycomet2]

Not higher but just and opposite - like the upward reaction force of the chair you're sitting on - never big enough to throw you upwards.

but if the supply voltage is sin t,and the current is (sin t)/R,and if

a)the back emf induced is just as the supply voltage but in opposite direction,then the back emf should be -sin t(or slightly lower due to resistance,but still sine curve), isn't??

b) if we consider by the differential equation,v=L dI/dt,then the back emf will be L(cos t)/R.Therefore the current must be sometimes flow against the supply voltage when cos t>sin t !?

OR,the hypothesis that current is proportional to supply voltage is wrong?

 

[sophiecentaur]

The current flowing around the circuit at any time will be governed by the supply volts minus the back emf. This will never be in antiphase with the original supply volts. Are you neglecting the existence of some resistance in the circuit?

 

[haleycomet2]

If the current is in phase with the supply voltage(sine curve),then the back emf will be differentiation of current(L di/dt),which is cosine curve --then the emf will be not in phase with supply voltage ?!
ps:I think that resistance will only affect the amplitude of curve but remains same trend.

 

[sophiecentaur]

The resistance will limit the back emf to less than the supply volts, that's all. Without resistance in the coil or the supply the problem is not soluble. It becomes another one of those questions involving irresistable forces and immovable objects.

 

[cabraham]

The resistance will limit the back emf to less than the supply volts, that's all. Without resistance in the coil or the supply the problem is not soluble. It becomes another one of those questions involving irresistable forces and immovable objects.

But the supply has already been stipulated as an ac source, sinusoidal waveform. Even w/o any resistance, i.e. superconducting windings, the inductor presents a reactance w/ no resistance. If the ac voltage source value is V, & the inductive reactance is X (X = omega*L), then I = V/jX. No problem arriving at a solution here.

Were you thinking a dc voltage source across the inductor? In that case the current would ramp upward towards infinity if no resistance were present. BR.

Claude

 

[sophiecentaur]

Yes, you're right about that. I haven't really been paying attention.

This is a simple question if one is prepared just to do the sums (assuming you can differentiate). Too many words have been expended on this and the Maths has been ignored. 'Verbal' explanations so often manage to fall down holes. (Just what I did, in fact.)

 

[haleycomet2]

What i can't understand is if I=V/jX =1/jX(sin t),then back emf will be Ldi/dt=L/jX(cos t),which is 90 degree out of phase of supply voltage.Doesn't back emf is always nearly equal (or at least in phase) to the supply voltage??
ps: jX =reactance right??
Thanks a lot.

 

[sophiecentaur]

X is reactance (a real value).
Impedance (Z) = R + jX (a complex value)

 

[sophiecentaur]

There will be a problem in calculating what you call "back emf" unless you introduce some resistance, somewhere. If you don't, the voltage you will measure across the inductor will be the same as the source voltage (because the constant voltage supply will 'insist' that it is that value. Back emf won't appear anywhere.
The 'back emf' will only show itself by its effect on the current that flows through the source resistance and, hence, some voltage drop at the terminals of the inductor.
If you work out the current through the circuit, it will be V/(R+jX) and work from there, you will get one 90degree phase change and then another - giving a back emf which is in antiphase.

 

[haleycomet2]

Referring to the graphs below(with or without resistance),the sign of current sometimes is in opposite with the voltage.Does this happened when back emf is greater than supply voltage or how to explain this?

ps:these pictures are originally from http://www.allaboutcircuits.com/vol_2/chpt_3/2.html

 

[sophiecentaur]

I think you are referring to instantaneous voltages (?). On the graphs you attached, you don't actually plot any 'back emf'. You are inferring it from the current on the graph. But, in the same way that the current that you plot is not in phase with the plotted input volts, why should you assume that the back emf is in phase with the (plotted) current which is causing it?
The concept of back emf is only a way of describing behaviour - like the reactive force when you push against a wall. From what you have written, you seem to be assigning it more importance - as if it's "really there" and that, somehow, it violates something.

My point about needing a series source resistor to do a proper analysis is that you could measure (/calculate) the voltage across the series resistor (which will, of course be less than the supply voltage) then this back emf you are after is the difference (vectorial / phasor) between the supply volts and the volts across the resistor.

Try relating all this to the bahaviours of RL and RC filters and to the high pass/low pass functions. If there is no resistance involved then there is a flat frequency response because the voltage source 'insists' on a whatever voltage it is producing.

 

[haleycomet2]

I think that back emf is not in phase with current,but is the differentiation of current.This is why i feel that it may not equal to the terminal voltage across inductor.
Besides,since current always flow in direction with the NET voltage.from the graph,sometimes the sign of supply voltage(or instantaneous voltage) is opposite with the sign of current.Therefore i think it may happen when back emf is larger than supply voltage,so the NET voltage is opposite as well and cause the current flow against the supply voltage.And this maybe is caused by the release of the energy stored in inductor.

 

[haleycomet2]

I think that back emf is not in phase with current,but is the differentiation of current.This is why i feel that it may not equal to the terminal voltage across inductor.
Besides,since current always flow in direction with the NET voltage.From the graph,sometimes the sign of supply voltage(or instantaneous voltage) is opposite with the sign of current.Therefore i think it happened when back emf is larger than supply voltage,so the NET voltage is opposite as well and cause the current flow against the supply voltage.And this maybe is caused by the release of the energy stored in inductor so the energy still is still conserved

 

[OmCheeto]

...
I've noticed that the "pushing/pulling current" heresy is very hard to get people to let go of, so I avoid it 24/7.

FWIW, I use the term "current drawn". I'll say that this motor draws 30 amps at start up & 5 amps steady state. As long as we understand that this is colloquial & not literal, all is well.

A person who sees current as being "pushed" seldom gives up such heresy.

Claude

Ok then, you are talking about me now.

How does one get a current flowing if one neither pushes nor pulls?

Sorry if I've misinterpreted the meat of your message. This thread reminds me somewhat of my foray into "How the hell do diodes work?" a few years back. I drilled down to the quantum level, and got totally lost, so I won't go there.(thread hijack preempted)

But on the most fundamental level, we have 4 copper atoms. Two pairs of dual copper atoms separated by space. To have a current flow, we have to move at least one electron from one atom to the other. This transfer of an electron will have an effect on an electron in the other copper atom pair(induction).

Of course by now, you are seeing where I'm coming from. If one neither pushes nor pulls, how do you get the electron to flow from atom A to atom B?

But this also introduces the fact that there is no such thing as a perfect anything. Getting an electron to move from atom A to atom B required a force, and knowing that electrons are not massless, this implies that there was a resistance. So we can remove the dreadful infinities that plague many a college textbook when discussing this topic on the macroscopic conceptual scale.

e^--->
A-B
(magical pixie magnetic force)
C-D
<--e^-​

dear FSM, please let me have one more get out of banned card for using the magical pixie magnetic force again...

 

[Bassalisk]

Ok then, you are talking about me now.

How does one get a current flowing if one neither pushes nor pulls?

Sorry if I've misinterpreted the meat of your message. This thread reminds me somewhat of my foray into "How the hell do diodes work?" a few years back. I drilled down to the quantum level, and got totally lost, so I won't go there.(thread hijack preempted)

But on the most fundamental level, we have 4 copper atoms. Two pairs of dual copper atoms separated by space. To have a current flow, we have to move at least one electron from one atom to the other. This transfer of an electron will have an effect on an electron in the other copper atom pair(induction).

Of course by now, you are seeing where I'm coming from. If one neither pushes nor pulls, how do you get the electron to flow from atom A to atom B?

But this also introduces the fact that there is no such thing as a perfect anything. Getting an electron to move from atom A to atom B required a force, and knowing that electrons are not massless, this implies that there was a resistance. So we can remove the dreadful infinities that plague many a college textbook when discussing this topic on the macroscopic conceptual scale.

e^--->
A-B
(magical pixie magnetic force)
C-D
<--e^-​

dear FSM, please let me have one more get out of banned card for using the magical pixie magnetic force again...

Well his point was, when we discussed about induced current that some of used analogy of pushing current when magnetic field was fading. No, he had a point current wasn't actually pushed like you would push a hand against the wall. But the reason we used it is because, for now we don't have a better word for it.

From my point of view, when current is fading through inductor, a magnetic field is fading, and that change in magnetic field induces a current that, well lol, it pushes it. Maybe better word is superposition of waves. Constructive interference. Hell i don't know anymore :D

But after this thread, i most certainly understand the concept. Maybe not the vocabulary of it but physics behind it I do

 

[OmCheeto]

Well his point was, when we discussed about induced current that some of used analogy of pushing current when magnetic field was fading. No, he had a point current wasn't actually pushed like you would push a hand against the wall. But the reason we used it is because, for now we don't have a better word for it.

From my point of view, when current is fading through inductor, a magnetic field is fading, and that change in magnetic field induces a current that, well lol, it pushes it. Maybe better word is superposition of waves. Constructive interference. Hell i don't know anymore :D

But after this thread, i most certainly understand the concept. Maybe not the vocabulary of it but physics behind it I do

Sometimes there is no understanding things. Things just are the way they are.

"Why" to the infinity, will just lead to madness.

--------------------------------
ya ne znam neeshta.
(= "I know nothing" in Serbski)

 

[sophiecentaur]

I can't see the difficulty in a back emf that happens to be bigger at times than the input volts. Energy is stored in the inductor and is released at a time when the input volts are not at their maximum. You don't get anything out than was put there earlier.

 

[haleycomet2]

I can't see the difficulty in a back emf that happens to be bigger at times than the input volts. Energy is stored in the inductor and is released at a time when the input volts are not at their maximum. You don't get anything out than was put there earlier.

Ya,this is what i think.However,i notice that the in the book ,it is written that

"To maintain the current,the applied supply voltage must be equal to the back emf.The voltage applied to the coil must therefore be given by V=L dI/dt."

when deduce the voltage of pure inductor circuit.
So I am confused.

 

[sophiecentaur]

I just re-read my last Post and there should be a "not" in the last sentence!

 

[tiny-tim]

hi haleycomet2!

… in the book ,it is written that

"To maintain the current,the applied supply voltage must be equal to the back emf.The voltage applied to the coil must therefore be given by V=L dI/dt."

when deduce the voltage of pure inductor circuit.

(this thread is sooo long that I'm not sure what we're talking about , but …) if this is a circuit with only a battery an inductor and no resistance, then KVL means that, at any instant, the "back emf" must equal the voltage

(hmm … having said that, i have vague memories of seeing comments that where there's an inductor, the electric field isn't conservative, so I'm not sure where that fits in )​