Why does current lag behind voltage in inductor?

[Bassalisk]

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

[LotusEffect]

Inductors react against a change in current. Applying a voltage to its terminals will produce a current that will then create a magnetic field like any other wire. An inductor is called as such because its magnetic coupling is high. In other words, the magnetic field it creates will have an effect on the element itself.

If the magnectic field varies with time (which is the case when you just applied a voltage to the inductor terminals), an electric field will be induced within the wire the counter the change in magnetic field. This E-field will tend to "stop" the current that would normally be present without the inductance effect. Thus current "lags" behind voltage. Too quick of change in current creates an e-field that decreases dI/dt.

You can see an inductor like a wheel that is free to spin due to the flow of a river. If the flow changes too quickly, the wheel, due to its inertia, will tend to keep spinning for a moment. The same is true if the water of the river goes from steady to flowing in a short instant.

[Zryn]

Lenz's Law @ Wikipedia (http://en.wikipedia.org/wiki/Lenz%27s_law)

"An induced current is always in such a direction as to oppose the motion or change causing it"

So you apply your voltage to an inductor and the coil shape acts to oppose the change in current. Note that the voltage that changes the current comes first, and then the induced current (and flux) change. Also note that 90 degrees out of phase only works for ideal inductors.

Another way of looking at it is that if you apply your source voltage to an inductor, V(S) = sin(wt) then the current must be i = sin(wt)/R, so by the inductor formula:

V(L) = L di/dt = L/R d sin(wt)/dt = L/R cos(wt)

And we know that cos(wt) is 90 degrees ahead of sin(wt).

[Bassalisk]

So basically, we apply AC to a inductor, and then current "pushes" more and more through conductor, it induces more and more induced current? and that induced current is in some way pushing back the current that was originally going through inductor?
But the voltage on the inductor stays the same?

[haleycomet2]

Lenz's Law @ Wikipedia (http://en.wikipedia.org/wiki/Lenz%27s_law)

Another way of looking at it is that if you apply your source voltage to an inductor, V(S) = sin(wt) then the current must be i = sin(wt)/R, so by the inductor formula:

V(L) = L di/dt = L/R d sin(wt)/dt = L/R cos(wt)

And we know that cos(wt) is 90 degrees ahead of sin(wt).

So actually the back emf in the circuit is initially larger than supply voltage?

[atomthick]

The idea that current lags is only true only if you use alternative current, just like Zryn correctly expressed through formulas, because of the special relation between sin and cos. If you however apply a different variation of voltage lets say Aln(t) you will get a V(L) = A L/(Rt) which doesn't seem to be delayed but instead totaly changed.

You should think of the lag only as a special case (in alternative current) to help you remember the relationship between current and voltage.

[Bassalisk]

Ok i think i got it. Now i need someone with good knowledge of complex area applied to e engineering. I just learnt from my classes that there is something called active and reactive resistance, power etc. I figured that active resistance is like a resistor. But i do not understand what reactive part is...
Thanks

[tiny-tim]

Hi Bassalisk! :smile:

In a resistor, voltage and current are dependent on each other, but in an inductor they are independent (so there is no resistance), and instead voltage is dependent on the rate of change of current: V = LdI/dt.

In a steady AC circuit, however, the rate of change of current is conveniently proportional to the current itself (and to the frequency), but 90° out of phase.

So the voltage is also 90° out of phase with the current. :wink:
I just learnt from my classes that there is something called active and reactive resistance, power etc. I figured that active resistance is like a resistor. But i do not understand what reactive part is...

Reactive resistance (or reactance, X) is the "imaginary part" of impedance (http://www.physicsforums.com/library.php?do=view_item&itemid=303) …

Z = R + jX …

a reactive component (inductor or capacitor) has no resistance (ie voltage does not depend on current), but has a coupling between V and dI/dt (for an inductor) or between I and dV/dt (for a capacitor), and the power through it (V times I) in a steady AC circuit cycles with twice the frequency of the circuit itself, and averages zero … this zero-average power is known as reactive power, I think because you "get it back". :wink:

[Bassalisk]

Inductors react against a change in current. Applying a voltage to its terminals will produce a current that will then create a magnetic field like any other wire. An inductor is called as such because its magnetic coupling is high. In other words, the magnetic field it creates will have an effect on the element itself.

If the magnectic field varies with time (which is the case when you just applied a voltage to the inductor terminals), an electric field will be induced within the wire the counter the change in magnetic field. This E-field will tend to "stop" the current that would normally be present without the inductance effect. Thus current "lags" behind voltage. Too quick of change in current creates an e-field that decreases dI/dt.

You can see an inductor like a wheel that is free to spin due to the flow of a river. If the flow changes too quickly, the wheel, due to its inertia, will tend to keep spinning for a moment. The same is true if the water of the river goes from steady to flowing in a short instant.

@Lotus if he sees this.

Can you explain this for the capacitors in AC circuits too? I think goes ahead by some value? again same question why? I know the equations.

Thanks

[Bassalisk]

Hi Bassalisk! :smile:

In a resistor, voltage and current are dependent on each other, but in an inductor they are independent (so there is no resistance), and instead voltage is dependent on the rate of change of current: V = LdI/dt.

In a steady AC circuit, however, the rate of change of current is conveniently proportional to the current itself (and to the frequency), but 90° out of phase.

So the voltage is also 90° out of phase with the current. :wink:


Reactive resistance (or reactance, X) is the "imaginary part" of impedance (http://www.physicsforums.com/library.php?do=view_item&itemid=303) …

Z = R + jX …

a reactive component (inductor or capacitor) has no resistance (ie voltage does not depend on current), but has a coupling between V and dI/dt (for an inductor) or between I and dV/dt (for a capacitor), and the power through it (V times I) in a steady AC circuit cycles with twice the frequency of the circuit itself, and averages zero … this zero-average power is known as reactive power, I think because you "get it back". :wink:

I think i got it. Thanks. So reason why this reactive resistance is attached to imaginary part, is because in principle it doesn't exist, in form of Ohm resistance, but this new kind of resistance due to inductance?

[tiny-tim]

Can you explain this for the capacitors in AC circuits too?

In an inductor, V is proportional to dI/dt, so (in a steady AC circuit) V leads I by 90°.

In a capacitor (http://www.physicsforums.com/library.php?do=view_item&itemid=112), I is proportional to dV/dt, so (in a steady AC circuit) I leads V by 90°. :wink:

EDIT: (I didn't notice your second post :redface:)
So by coupling u DON'T mean depending?

No, they mean the same thing, I was just using a different word.

V depends on dI/dt. :smile:

[Bassalisk]

In an inductor, V is proportional to dI/dt, so (in a steady AC circuit) V leads I by 90°.

In a capacitor (http://www.physicsforums.com/library.php?do=view_item&itemid=112), I is proportional to dV/dt, so (in a steady AC circuit) I leads V by 90°. :wink:

EDIT: (I didn't notice your second post :redface:)


No, they mean the same thing, I was just using a different word.

V depends on dI/dt. :smile:

Yea i understood and edited. Thanks ! :D

[tiny-tim]

So reason why this reactive resistance is attached to imaginary part, is because in principle it doesn't exist, in form of Ohm resistance, but this new kind of resistance due to inductance?

(It's all measured in ohms, of course, but yes …)

yes, reactive resistance isn't the V/I resistance we're used to, so it has to be dealt with separately.

As to why (and how) it's imaginary, that's a mathematical trick (which only works in steady AC circuits) … see the PF Library on impedance (http://www.physicsforums.com/library.php?do=view_item&itemid=303) :wink:

[Bassalisk]

(It's all measured in ohms, of course, but yes …)

yes, reactive resistance isn't the V/I resistance we're used to, so it has to be dealt with separately.

As to why (and how) it's imaginary, that's a mathematical trick (which only works in steady AC circuits) … see the PF Library on impedance (http://www.physicsforums.com/library.php?do=view_item&itemid=303) :wink:

Will do thanks tim !

[sophiecentaur]

So actually the back emf in the circuit is initially larger than supply voltage?

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.

[Jiggy-Ninja]

I think i got it. Thanks. So reason why this reactive resistance is attached to imaginary part, is because in principle it doesn't exist, in form of Ohm resistance, but this new kind of resistance due to inductance?
"Imaginary" is just a name, don't read too much into it. i 1 is just as "real" as any other number.

I don't think that i has any special physical significance like other constants such as \pi, it's just a bit of a mathematical trick that makes it easy to do math with waves. In addition to its amplitude, the waves' phase is important as well. Since reactance is 90 degrees out of phase with resistance, it is attached to the imaginary pat of the equations.

1What do you do when you need to start a sentence with a lowercase constant? Uppercase would be technically wrong, but lower case just looks weird.

[LotusEffect]

The idea that current lags is only true only if you use alternative current, just like Zryn correctly expressed through formulas, because of the special relation between sin and cos. If you however apply a different variation of voltage lets say Aln(t) you will get a V(L) = A L/(Rt) which doesn't seem to be delayed but instead totaly changed.


I dont know what you just did there but if you apply V(t) = A ln(t) to an inductor, the current will be I(t) = 1/L * (t ln(t) - t). Current in an inductor is the integral of voltage.


@Lotus if he sees this.

Can you explain this for the capacitors in AC circuits too? I think goes ahead by some value? again same question why? I know the equations.

Thanks
You mean use some sort of analogy like the one of the spinning wheel for an inductor? I can't find one, but what I can tell is that in a capacitor, voltage "lags" vehind current because voltage across a capacitor terminals depends on the total amount of charge that accumulated on the plates. If you quickly change the current flowing through the capacitor, it takes a short instant for the charges to "leave" the cap. So a capacitor stores energy in the form of accumulated charges and an inductor stores energy in the form of accumulated magnetic field.


Impedances are a very neat trick to calculate currents and voltages in an ac circuit. When dealing with signals that all have the same frequency, it's clever to express them and impedances using phasors. Phasors are just complex numbers, and when expressed in polar form, they make calculations of rms values and phase angle of signals very easy.

[Jiggy-Ninja]

You mean use some sort of analogy like the one of the spinning wheel for an inductor? I can't find one,
A spring (https://ccrma.stanford.edu/~jos/fp3/Mechanical_Equivalent_Capacitor_Spring.html) or a rubber diaphram (http://en.wikipedia.org/wiki/Hydraulic_analogy#Component_equivalents).

[tiny-tim]

Hi Jiggy-Ninja! :smile:
I don't think that i has any special physical significance like other constants such as \pi, it's just a bit of a mathematical trick that makes it easy to do math with waves. In addition to its amplitude, the waves' phase is important as well. Since reactance is 90 degrees out of phase with resistance, it is attached to the imaginary pat of the equations.

Yes, j (or i) describes the physical attribute of being +90° out of phase. :smile:
1What do you do when you need to start a sentence with a lowercase constant? Uppercase would be technically wrong, but lower case just looks weird.

Patient to doctor: it hurts when I do that!
Doctor to patient: then don't do that!

Then don't start a new sentence! :rolleyes: …

"Imaginary" is just a name, don't read too much into it … i is just as "real" as any other number. :wink:

(alternatively, use j ! :biggrin:)
… a rubber diaphram.

From the PF Library on capacitor (http://www.physicsforums.com/library.php?do=view_item&itemid=112) …

Fluid mechanics analogy:

In fluid mechanics, a capacitor is analogous to a diaphragm blocking a pipe.

Water cannot pass through the diaphragm.

But pressure suddenly applied on one side will make the diaphragm bulge, so that water continues to flow "into" the diaphragm on one side, and "away from" the diaphragm on the other side, until the diaphragm reaches its maximum bulge for that pressure.

The volume of the bulge, divided by the pressure, is the capacitance.

The energy stored is half the volume of the bulge times the pressure.

The displacement current is rate at which the volume of the bulge is increasing (and is zero once the maximum bulge is reached).

[Bassalisk]

U guys should get paid seriously XD Thanks, i got everything clear now!!!!

[Jiggy-Ninja]

Hi Jiggy-Ninja! :smile:
Hi fictional-character-from-a=Charles-Dickens-story-who-has-a-terminal-illness! :frown:
Yes, j (or i) describes the physical attribute of being +90° out of phase. :smile:
What I'm getting at is that conceptually, \pi is pretty easy to understand. It's a ratio of lengths, and can be very easily visualized. (I'm a very visual thinker)

What \sqrt{-1} has to do with being 90° out of phase is a leap of understanding that I have yet to make. All I know is that it apparently works.
Patient to doctor: it hurts when I do that!
Doctor to patient: then don't do that!

Then don't start a new sentence! :rolleyes: …
Completely useless, smart-*** answer to a half-serious question? You and I are going to get along just perfectly.
(alternatively, use j ! :biggrin:)
I ran into i first, so that's what I use by habit. No point in having two symbols for the same weird number.

Or, just go with Japanese. Some of the hiragana are quite pretty. I especially like み for some reason. I'll use that for my complex numbers instead.
U guys should get paid seriously XD Thanks, i got everything clear now!!!!
Alas, don't I know it. I'm basically an unpaid teacher's assistant in my classes. Helping other people who are confused is a near-irresistible impulse for me.

[Bassalisk]

Well, in mathematics Complex numbers C are extension of Real numbers.

Complex numbers have special way of multiplying and adding together such that u have a consequnce: when u take a square root of -1 is i. Now that is NOT a definition of i. Definition of i is that i is for complex numbers what 1 is to real numbers.

Real definition of i is long and we would have to go in calculus analysis.

And there is a reason for j. In electricity u have I for current, sometimes written in small letters i. U don't want to get mixed up, that why some ppl use j instead of i.

Complex numbers come in pairs. By the time engineers thought of using complex numbers, they were fully developed.

I don't think that there is some direct connection between what u said, Jiggy, I don't even think it could be. Think about it, complex numbers were mainly made to cover that area where u can't do square roots of negative numbers, those were first reasons for making complex numbers.

Engineers came and said, heeey we can use that etc etc. I only find analogy in reactive resistance being bound to complex area. Why? because it is not REAL resistance, like due to conductivity of matter.

It is some new kind of resistance that it needed to be distinct from ohmic resistance.


I am too kinda guy that wants to visualize everything. That's why I have so many questions that are mainly related to theory, not formulas.

[Bassalisk]

Another question:

When we have a current going through inductor, at first we have a change in magnetic field. That change self-induces a current that opposes original current. Now, when current is fading, another change in flux, will that change now try to push(in the same direction as current) the original current?

[Jiggy-Ninja]

Another question:

When we have a current going through inductor, at first we have a change in magnetic field. That change self-induces a current that opposes original current. Now, when current is fading, another change in flux, will that change now try to push(in the same direction as current) the original current?
That change self induces a voltage that opposes the change.

And yes, as the current fades, the flux will collapse and induce a voltage that tries to keep pushing the current forward.

[LotusEffect]

Another question:

When we have a current going through inductor, at first we have a change in magnetic field. That change self-induces a current that opposes original current. Now, when current is fading, another change in flux, will that change now try to push(in the same direction as current) the original current?

Exactly, as the spinning wheel analogy suggests!

[Bassalisk]

Physics is phun!

[cabraham]

I would suggest that the reason current lags voltage in an inductor has to do most w/ energy. An ideal inductor would possess 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.

Of course, real world inductors have capacitance & vice-versa. But at low frequencies a good inductor stores much more energy in its inductance vs. its capacitance. I would advise any interested parties to read peer-reviewed texts & articles for reference info. All this talk about current "being pushed" is utter nonsense. Current isn't "pushed".

Claude

[LotusEffect]

This is a good post and great addition to the discussion^^.

But btw, we all know that current isn't "pushed" :P. But sometimes using familiar expressions help understand the problem :). We also often say that toasters and ovens "pull" a lot of current!

[epenguin]

1What do you do when you need to start a sentence with a lowercase constant? Uppercase would be technically wrong, but lower case just looks weird.


i wonder if this looks better?

[Bassalisk]

All this talk about current "being pushed" is utter nonsense. Current isn't "pushed".

Claude

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.

[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 possess 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 cant 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. :grumpy:

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. :grumpy:

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! :wink:
… 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 :redface: that i'm not sure what we're talking about :confused:, 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 :smile:

(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 :confused:)

[Metaleer]

hi haleycomet2! :wink:


(this thread is sooo long :redface: that i'm not sure what we're talking about :confused:, 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 :smile:

(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 :confused:)

You're probably thinking of how Walter Lewin (MIT Physics professor) argues (rather convincingly, I must say) that in the presence of inductors, Kirchhoff's voltage law does not apply, since this law applies for conservative fields, and changing B-fields (inductors) mean that the field is no longer conservative (as the curl of the E-field no longer vanishes, by the Faraday-Lenz law). However, you can still use the Faraday-Lenz law to see if this statement about the back emf and the voltage is true.

[sophiecentaur]

It still bothers me that some people see the emf as a 'problem'. Perhaps the definition of volts as "joules per coulomb" and just accept what you get; it is just the energy situation at different places in the circuit.

[haleycomet2]

Could anyone suggest any link or books which have a deeper introduction of inductor(i have read“all about circuit” ,"hyperphysics" website,and A-level physics by Nelkon and Parker)?I am sorry for troubling u all and maybe i need time to study more and think more to understand this.
Thank you.

[cabraham]

Ok then, you are talking about me now. :grumpy:

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.........

I responded to this post a day or 2 ago, but I hit "preview post" instead of "submit post". It was never entered. So here it is.

Initially some type of force is needed to commence conduction. Electrons, in the case of metals, & holes and/or ions for other media, must begin motion, in order to transfer their energy to other charges, enabling them to conduct.

The initial energy needed to do this comes from a redox reaction in a battery, or from mechanical input enrgy for a generator. You've probably seen those desktop gadgets w/ 5 or so steel balls suspended on strings. They touch each other, so that if 1 ball is moved outward, it strikes the 2nd ball, & the 5th ball at the other end rises. It eturns to its starting point, & the 1st ball rises, etc. The principle here is transfer of energy & momentum. Of course somebody had to provide energy to get the process started.

Current conduction is similar to the suspended balls gadget. Once charges are given energy to put them in the conduction band, that energy is transferred to other particles. The electrons conducting in a metal are not being "pushed". They are energized initially, then transfer said energy to other particles.

As far as resistance goes, that involves atomic collisions. Electrons collide w/ the lattice, energy is dissipated as photons are released. The photon emission is in the IR wavelength around 5 micron, & is felt as heat.

So if an inductor is energized, it tends to maintain a constant current. If the source is disconnected & the inductor shorted, the current will remain constant forever if no resistance were present. But, for a resistive inductor, electrons conduct & bang into the lattice losing energy. This energy is radiated as heat. Hence the energy in the inductor is decreasing, as is the current, since W = L*I^2/2.

Did this help?

Claude

[martix]

I guess that's a common issue with a lot of people, that and capacitors.

Got one for you.(though I don't know if it's been mentioned already since I won't bother reading through the whole thread)

It is just my intuitive interpretation of the concepts.
Think of an inductor as the electrical equivalent of a flywheel. It's a great analogy for me and I think it works on many levels.
Just as a capacitor's mode of operation can be compared to that of a spring.

Where one deals with electrical energy, so does the other deal with its mechanical counterpart(here's hoping that those are concepts more intuitively familiar to you).

[Bassalisk]

I responded to this post a day or 2 ago, but I hit "preview post" instead of "submit post". It was never entered. So here it is.

Initially some type of force is needed to commence conduction. Electrons, in the case of metals, & holes and/or ions for other media, must begin motion, in order to transfer their energy to other charges, enabling them to conduct.

The initial energy needed to do this comes from a redox reaction in a battery, or from mechanical input enrgy for a generator. You've probably seen those desktop gadgets w/ 5 or so steel balls suspended on strings. They touch each other, so that if 1 ball is moved outward, it strikes the 2nd ball, & the 5th ball at the other end rises. It eturns to its starting point, & the 1st ball rises, etc. The principle here is transfer of energy & momentum. Of course somebody had to provide energy to get the process started.

Current conduction is similar to the suspended balls gadget. Once charges are given energy to put them in the conduction band, that energy is transferred to other particles. The electrons conducting in a metal are not being "pushed". They are energized initially, then transfer said energy to other particles.

As far as resistance goes, that involves atomic collisions. Electrons collide w/ the lattice, energy is dissipated as photons are released. The photon emission is in the IR wavelength around 5 micron, & is felt as heat.

So if an inductor is energized, it tends to maintain a constant current. If the source is disconnected & the inductor shorted, the current will remain constant forever if no resistance were present. But, for a resistive inductor, electrons conduct & bang into the lattice losing energy. This energy is radiated as heat. Hence the energy in the inductor is decreasing, as is the current, since W = L*I^2/2.

Did this help?

Claude

Can you explain what field of electrical engineering are you working on? I study electrical engineering, first year, telecommunications department and they don't teach me that stuff. They only went so far when explaining electricity, I almost failed my exams because I didn't focus on studying, I focused on understanding things that I've learned.

And yes, this makes things very clear. Can you recommend me some book(s) that you have studied from? I will buy them online if i have to, just give me the names.

Thanks

[cabraham]

I am a broad EE generalist, w/ primary focus on analog & power electronics. I develop motor drives, smps (switch mode power supplies), microcontroller & dsp based systems, analog filters, to name a few.

Understanding quantum mechanics, "qm", is something nobody has yet achieved. To fully understand inductance, conduction, energy bands, thermo, etc., involves deep level of qm. The late great Richard Feynmann, one of the giants of the 20th century science community, flatly stated that he does not fully comprehend qm, & that anyone who claims otherwise is fooling nobody but themself. I frankly admit before the world that qm is beyond me.

When I took modern physics as an undergrad, as well as e/m fields, I just accepted what was taught w/o questioning or attempting to comprehend it fully. If the phy prof says this is how the science community sees it, I nod my head & say "yes sir." We can explain things down to a level where we cannot go further. Axioms are developed based on verifiable repeatable observation/testing, & all else is derived from those axioms. One cannot "prove" or explain an axiom in terms of something more fundamental because the most fundamental quantities we can detect give birth to the axiom itself.

Books I'd recommend are any uni-approved EE fields texts as well as physics fields texts. Also, circuit theory texts give a great mAcroscopic explanation of inductors, but fields texts give a better mIcroscopic view. Also, good texts on energy conversion, dealing w/ motors & generators, transformers, solenoids, etc. are great references. Fitzgerald, Kingley, & Umans text "Electric Machinery" is quite good. I just had Dr. Umans for a power course spring 2010. It was great.

Anyway, I hope I've helped. BR.

Claude

[Bassalisk]

I am a broad EE generalist, w/ primary focus on analog & power electronics. I develop motor drives, smps (switch mode power supplies), microcontroller & dsp based systems, analog filters, to name a few.

Understanding quantum mechanics, "qm", is something nobody has yet achieved. To fully understand inductance, conduction, energy bands, thermo, etc., involves deep level of qm. The late great Richard Feynmann, one of the giants of the 20th century science community, flatly stated that he does not fully comprehend qm, & that anyone who claims otherwise is fooling nobody but themself. I frankly admit before the world that qm is beyond me.

When I took modern physics as an undergrad, as well as e/m fields, I just accepted what was taught w/o questioning or attempting to comprehend it fully. If the phy prof says this is how the science community sees it, I nod my head & say "yes sir." We can explain things down to a level where we cannot go further. Axioms are developed based on verifiable repeatable observation/testing, & all else is derived from those axioms. One cannot "prove" or explain an axiom in terms of something more fundamental because the most fundamental quantities we can detect give birth to the axiom itself.

Books I'd recommend are any uni-approved EE fields texts as well as physics fields texts. Also, circuit theory texts give a great mAcroscopic explanation of inductors, but fields texts give a better mIcroscopic view. Also, good texts on energy conversion, dealing w/ motors & generators, transformers, solenoids, etc. are great references. Fitzgerald, Kingley, & Umans text "Electric Machinery" is quite good. I just had Dr. Umans for a power course spring 2010. It was great.

Anyway, I hope I've helped. BR.

Claude

U were more than helpful. But I myself am very passionate about learning. My college department offers 5% of QM that I want to know. I am self-taught at home QM to get at least a glimpse how something works. My dream is to study QM, but there is no such college here. Only parts of some departments go so far.

Well I understand that you don't have to know QM to actually understand something. U can accept it by heart. But here is the thing. I want to understand. I think I am the only one amongst 300 students that really go down to quantum level to understand some processes.

My assistants told me: kid you are going to go crazy, you cannot understand everything we are trying to teach you. I said: So be it.


Now you see why I bug this thread so much...

Thanks for the book, I will check it out, you were very helpful. High level opinions like yours here should be highlighted.

[sophiecentaur]

If you really think you can square the effects of Inductance with QM then you are welcome to try. Frankly, anyone who could do that should have a pretty thorough understanding of the Classical approach- Maxwell etc..
The good thing about the Classical approach is that all it demands is the ability to understand the wonderful world of Integral Calculus and also some ability with vectors. There are many basic EM theory books to degree level which will get you a fair way to the way fields and structures interact. I look at the ones I bought at Uni (mid '60s) and it's amazing just how much the classical approach can do for you. Snag is, you can't wave yer arms about with EM theory. It's far too businesslike and not quite so much open to 'interpretation', which is why QM appeals to so many people as a conversation piece.

[cabraham]

If you really think you can square the effects of Inductance with QM then you are welcome to try. Frankly, anyone who could do that should have a pretty thorough understanding of the Classical approach- Maxwell etc..
The good thing about the Classical approach is that all it demands is the ability to understand the wonderful world of Integral Calculus and also some ability with vectors. There are many basic EM theory books to degree level which will get you a fair way to the way fields and structures interact. I look at the ones I bought at Uni (mid '60s) and it's amazing just how much the classical approach can do for you. Snag is, you can't wave yer arms about with EM theory. It's far too businesslike and not quite so much open to 'interpretation', which is why QM appeals to so many people as a conversation piece.

Yes I agree w/ you that the classical approach per Maxwell et al offers a wealth of insight. For practical engineering applications, classical more than suffices. I guess we all got off the deep end delving into quantum theory. It's interesting to ponder, but as you mentioned, the study, analysis, & design of transformers, solenoids, filters, machines, etc., can be done full justice using classical methods.

Maxwell's axioms stand like a Gibraltar, today, yesterday, & tomorrow. Thanks to you & all for a most interesting discussion.

Claude

[RANA WAJID]

as we know that the ohmic resistance of the inductor is very low.
when we apply some potential or voltages to the coil the coil energies and a flux is produced in it.
There are three types of effects when we apply voltages to the coil.
1) As according to the self induction when due to the change in direction or magnitude of flux then emf induces in that coil.
2) we know that when electricity is given to any motor than back emf induces in that motor so here back emf also produced and due to which a current also flows through the inductor which is opposite in direction to the supply current.this back current provides some resistance in the flow of current that's why current lags from voltage in inductors.
3) third and last one effect relates with the LENZ's law according to which current always opposes its own generating process.
so by the above given reasons we say that the current lags from the voltage in the inductor so the back current is partially stopped that current.
Due to that partial stop of current voltages become leading.
THIS ANS IS GIVEN TO ME BY OUR GOOD TEACHER
MUSSADIQ ALI RAZA

[jim hardy]

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

touchable and intuitive, eh?
All you need is to believe Lenz's law.

here's how i came to believe it at the primal level. I felt it.
You need a decent sized 115 volt transformer, maybe a pound or two, and an analog multimeter with RX1 scale such as Simpson 260.
Or, lacking a meter, a D cell battery and a smallish transformer.

Set the multimeter on RX1, zero it and connect to the transformer's primary.
You will see the meter move to indicate the winding resistance of just a few ohms.
Repeat until you get a feel for how fast the needle moves.
Then reverse the leads, and you should notice a short hesitation before needle begins its travel.
Note difference in delay when you reverse or dont reverse leads between readings .

That delay is the transformer's inductance opposing the (increasing) current flow from the meter. A Simpson 260 on RX1 scale will push about 100 milliamps into low ohms. Lenz's law says inductance will oppose change in flux. That's the delay you observe on the meter.
When you dont reverse leads, the transformer is less able to resist because core was left mildly magnetized, so there's less change in flux than when you do reverse leads.

Now pinch the two transformer leads beneath fingers of one hand.
Apply multimeter again and note the shock you feel when removing the test lead.
That is the inductance opposing the reduction of flux - it will literally "Bite the hand...."

>>>>>NOTE --use one hand, dont ever intentionally pass current through your chest.<<<<<

if you dont have a multimeter , use a smaller transformer and a D cell.....
>>> Repeat:: smaller transformer <<<

feeling that shock should help you believe that inductance vigorously opposes change in flux.... quite vigorously.

Now - back to definition of inductance

inductance (L) = flux linkages per ampere
L = n * Phi / I ;; n=turns, I = amps, Phi = flux
so flux = I * L/ n ;; which says ( L and n being constants ) current and flux are in proportion no time delay
so the inductor tries to maintain flux by maintaining current;
which it does by producing voltage that you can feel

and it's symmetric, inductance will oppose an increase or a decrease in current.


An ideal inductor could hold out forever but a real one reaches limit on current through its copper or flux through its core.
Recall that a sinewave is a mathematical special case, where time delay becomes phase...

That simple experiment should help you believe the formulas.
But - use a transformer you can pick up with one hand. A big one would be dangerous.

or just take my word for it.....



old jim

[Bassalisk]

touchable and intuitive, eh?
All you need is to believe Lenz's law.

here's how i came to believe it at the primal level. I felt it.
You need a decent sized 115 volt transformer, maybe a pound or two, and an analog multimeter with RX1 scale such as Simpson 260.
Or, lacking a meter, a D cell battery and a smallish transformer.

Set the multimeter on RX1, zero it and connect to the transformer's primary.
You will see the meter move to indicate the winding resistance of just a few ohms.
Repeat until you get a feel for how fast the needle moves.
Then reverse the leads, and you should notice a short hesitation before needle begins its travel.
Note difference in delay when you reverse or dont reverse leads between readings .

That delay is the transformer's inductance opposing the (increasing) current flow from the meter. A Simpson 260 on RX1 scale will push about 100 milliamps into low ohms. Lenz's law says inductance will oppose change in flux. That's the delay you observe on the meter.
When you dont reverse leads, the transformer is less able to resist because core was left mildly magnetized, so there's less change in flux than when you do reverse leads.

Now pinch the two transformer leads beneath fingers of one hand.
Apply multimeter again and note the shock you feel when removing the test lead.
That is the inductance opposing the reduction of flux - it will literally "Bite the hand...."

>>>>>NOTE --use one hand, dont ever intentionally pass current through your chest.<<<<<

if you dont have a multimeter , use a smaller transformer and a D cell.....
>>> Repeat:: smaller transformer <<<

feeling that shock should help you believe that inductance vigorously opposes change in flux.... quite vigorously.

Now - back to definition of inductance

inductance (L) = flux linkages per ampere
L = n * Phi / I ;; n=turns, I = amps, Phi = flux
so flux = I * L/ n ;; which says ( L and n being constants ) current and flux are in proportion no time delay
so the inductor tries to maintain flux by maintaining current;
which it does by producing voltage that you can feel

and it's symmetric, inductance will oppose an increase or a decrease in current.


An ideal inductor could hold out forever but a real one reaches limit on current through its copper or flux through its core.
Recall that a sinewave is a mathematical special case, where time delay becomes phase...

That simple experiment should help you believe the formulas.
But - use a transformer you can pick up with one hand. A big one would be dangerous.

or just take my word for it.....



old jim

You got my attention. I understood mostly of it. I will definitely try this. :D

[jim hardy]

I understood mostly of it....

thanks.

i sorta swapped terms on ya there, using current and flux interchangeably before showing that they are indeed one another's image...
but i think that is a key detail to grasp when figuring out inductance.
grasping that little insignificant(?) point will help you understand how real inductors depart from ideal ones.

Keep it simple. (That helps things "go well".)


old jim

[psparky]

I didn't get to read the whole thread...but will throw in my two cents nonetheless.

Reactance of an inductor is JWL.....or WL <90 degrees.

V=IR......In this case R = JWL

When you divide the voltage by 90 degrees....you get a minus 90 degrees.

Therefore current is lagging voltage.

A capacitor does just the opposite 1/(JWC).

You get a current vector in the plus 90 degree direction. This is how power factor correction is achieved.

Any questions?

[sophiecentaur]

So many of you guys don't want to get your feet wet in Calculus. However, if you consider that the voltage that appears across an inductor is proportional to the rate of change of the current, then the current will be the integral of the voltage. When you apply this to a sinusoidal signal, you get exactly the lead and lag effects you would expect.
Why is that not a perfectly good explanation?

[Bassalisk]

This thread is almost 8 moths old. In these 8 months my calculus became very good. So this lagging physically I now understand, but with now good calculus its even simpler.But I do not regret for asking this to be explained on physical level.

[sophiecentaur]

Can you claim to be merely 'physical' once you have introduced sines and phases?

[psparky]

To sophiecentar.....your explanation is fine....

I just explained it in a different way that proves it mathematically as well.....and it also spurs thoughts toward power factor correction.

[Bassalisk]

Can you claim to be merely 'physical' once you have introduced sines and phases?

Well, all I'm saying is that I had troubles with math. I had to get the exam ready. I couldn't learn whole calculus in a week, so i tried to find a common sense and use my current knowledge of physics to get a feeling for that lag.

I did write that I knew about the formula for voltage across the inductor, but did I had a true feeling and knowledge of what derivative and integral means? no.

All I knew was, when I do derivative of a sine, i get a cosine. That is as far as my mind went. Later, when I finished calculus course, and I had to study for my final exam, I had to learn like 250 pages of pure calculus to pass. This final exam is not written, you talk with professor and he can ask you anything.

I had to learn all those theorems, fundamental theorems of derivatives, integrals, derivatives and calculus in general(Fermat's La grange's Cauchy's Cantor's need I go on?) . Did that help me understand a, I may say now simple problem like lag in inductor ? Yes ! Of course it did. But at the point I was asking this question, 8 months ago, I didn't have as good math as I do now.

And yes, I can say that I can "feel" the sine function now. Its not just another function for me.

[sophiecentaur]

OK but is "j" 'physical'? The idea of complex numbers comes way along the line in Maths, I should have thought.

Glad to hear you have laid the ghost of hard Maths. One step at a time and it will yield!

[Bassalisk]

OK but is "j" 'physical'? The idea of complex numbers comes way along the line in Maths, I should have thought.

Glad to hear you have laid the ghost of hard Maths. One step at a time and it will yield!

Yea j isn't physical. I got that. I understood that its only a good tool that somehow works very well when going back and forth between frequency and time domain.

I am very happy that I truly understand how j is incorporated.

Not once I found myself asking: "There must be SOME kind of relation between reactive resistance and imaginary numbers, other than mathematical. This square root of number one, the whole idea of imaginary numbers, and the way they are set up, there must be something there. I know that nobody can answer this question for me. I do know that currently it is just said that it works, and that there is no good reason for why is reactive part imaginary and I know great minds have thought this through and it works, but still you have that little tingling feeling in the back of your head, every time you think of it"

But one time I did that, I went deeper and deeper and deeper, then I stopped. Where did I stop? At the axioms of math. And there are no answers there. They are axioms. If people want to question this relation, then ask a question: What is number? Why are numbers defined like this, why -2 smaller than 2 etc. This just math, pure and purest science that was, is, and will ever exist.

[Bassalisk]

But then again, this science and all this math I learned, It affected me as a person. I am questioning the existence of God, luck and all that stuff that makes life easier. I am beginning to think deterministically. All this is very hard on me.

[sophiecentaur]

Aren't we just differentiating between what's very familiar, what's not so familiar and what we jus can't grasp at all? It's all very personal at this level.
If you 'feel' the result of some maths because you've done it so often that it's second d nature then I guess it becomes like the sums you do in your head when you're running downstairs. You just 'do it'. I suppose something like that could be described as Physical.
But is it really?
To my mind, truly 'physical' models are more Concrete Operational (Piagetian Cognitive Levels - google him) and don't support useful hypothesising. Mostly, people on these fora are using more (possibly a private, personal) maths than they are aware of. For Physical, read 'Familiar'.
Formal Maths is useful / essential for seriously progressing but it's also a useful common language because it is less likely to cause misunderstanding. I can't think, for instance, of a more concise term than 'Integral' to describe basically what's going on in many situations.

I think that, to have made the comments you did, implies a comfortable level of Formal Operational thought. The same goes for a lot of other contributors. (Ye Gods - was that a compliment? I'd better watch myself.)
Of course, Formal Operational thought may not actually imply 'reasonableness'. haha

[Bassalisk]

Aren't we just differentiating between what's very familiar, what's not so familiar and what we jus can't grasp at all? It's all very personal at this level.
If you 'feel' the result of some maths because you've done it so often that it's second d nature then I guess it becomes like the sums you do in your head when you're running downstairs. You just 'do it'. I suppose something like that could be described as Physical.
But is it really?
To my mind, truly 'physical' models are more Concrete Operational (Piagetian Cognitive Levels - google him) and don't support useful hypothesising. Mostly, people on these fora are using more (possibly a private, personal) maths than they are aware of. For Physical, read 'Familiar'.
Formal Maths is useful / essential for seriously progressing but it's also a useful common language because it is less likely to cause misunderstanding. I can't think, for instance, of a more concise term than 'Integral' to describe basically what's going on in many situations.

I think that, to have made the comments you did, implies a comfortable level of Formal Operational thought. The same goes for a lot of other contributors. (Ye Gods - was that a compliment? I'd better watch myself.)
Of course, Formal Operational thought may not actually imply 'reasonableness'. haha

This forum helped me in many ways, other than EE. These posts I read, like yours, are very well written. And I really stress my brain to truly understand what you are trying to say, as you may assume English is not my first language.

I will of course progress as I go to upper years. I will of course be more familiar with math and I will start to think mathematically more, and less physically.

Thank you for your suggestions, I will definitely research them out.

[sophiecentaur]

Why thank you kind sir. Your own English is not arf bad at all. You make sense and don't make me smile. What more can one ask for?

[Bassalisk]

Why thank you kind sir. Your own English is not arf bad at all. You make sense and don't make me smile. What more can one ask for?

No problem at all. Thats why you are Science Advisor and I am student with a lot of questions. Knowledge is my reward sir. :)

[Pablo Verdugo]

I'll try to use the perspective of power. As far as ii know, a conductive predominant circuit has positive reactive power, so S=P+jQ. Now, in per unit, we have S=VI*
By substituting terms I=S*/V* which means I=(P-jQ)/V*
S=P-jQ gives you a negative angle so current lags voltage, if you want to assume an infinite bar which would make the voltage angle equal to zero.

This may not be the explanation you were looking for, but it's just another perspective.

[sophiecentaur]

No problem at all. Thats why you are Science Advisor and I am student with a lot of questions. Knowledge is my reward sir. :)

omg - a mutual appreciation society!

[jim hardy]

what an interesting couple pages.

i'm not anti-math but am sympathetic toward those who struggle with it.

being mildly autistic, my awkwardness made math more difficult for me than it should have been. simple arithmetic mistakes scuttled many a calculus problem that i'd set up correctly but blew the evaluating part from a dropped sign or something.

result is i am real skeptical of formulas unless i can "feel" them.

when you're as dumb as me you have to work twice as hard as normal people and that's why i try to explain things simply - if it keeps somebody from giving up it's worthwhile.

for anybody stuggling with concept behind operator j ;
here's what i decided felt right:
multiplying by operator j shifts phase 90 degrees
multiplying twice shifts you 180 degrees,
which is exactly same as multiplying by -1
so obviously j is sqrt(-1) , for when you multiply it by itself you get -1 and that's a square root.
And of course it's imaginary because everybody knows negative numbers don't have square roots.

works for me. I'm no Euler.
but i learn from most everybody i meet.
great discussion guys , thanks.



old jim

[Bassalisk]

what an interesting couple pages.

i'm not anti-math but am sympathetic toward those who struggle with it.

being mildly autistic, my awkwardness made math more difficult for me than it should have been. simple arithmetic mistakes scuttled many a calculus problem that i'd set up correctly but blew the evaluating part from a dropped sign or something.

result is i am real skeptical of formulas unless i can "feel" them.

when you're as dumb as me you have to work twice as hard as normal people and that's why i try to explain things simply - if it keeps somebody from giving up it's worthwhile.

for anybody stuggling with concept behind operator j ;
here's what i decided felt right:
multiplying by operator j shifts phase 90 degrees
multiplying twice shifts you 180 degrees,
which is exactly same as multiplying by -1
so obviously j is sqrt(-1) , for when you multiply it by itself you get -1 and that's a square root.
And of course it's imaginary because everybody knows negative numbers don't have square roots.

works for me. I'm no Euler.
but i learn from most everybody i meet.
great discussion guys , thanks.

old jim

Well you are "dumb" as I am. Because I can only work with formulas if I can "feel" them too. Mathematical and physical ones, both I have to "feel".

[psparky]

I'm not sure I have ever needed to "feel" math....just understand it.

To me math has come easy....but I certainly "feel" for those who trouble with it.

In alegebra there is one basic rule...."what you do to one side of the equation...you do to the other side".

That and there are only two things you can do in math......add or multiply.

Subtracting is addition of the opposite.....division is multipication of the reciprical.

And yes, there are a ton of little rules, but the above is pretty much the basics....I "feel".

[sophiecentaur]

'multiply' is just a series of additions, in any case.
But ordinary arithmetic rules are not used in all maths - so there is a tiny bit more to it. :cool:

[psparky]

I agree.

You can certainly go far with the basics I mentioned.....differetial equations, calc 3 and so on.

But yes....it is a bit more complicated.

And actually the math is simple eventually....learning how to set up the problems in real life....or in story problems is the trick.