# HOW does voltage lead current in an inductive circuit?

#### BR-549

Joined Sep 22, 2013
4,938
Yes....I finally got the translation from our cousins. My cobwebs are apparent now. I thought coax at first, but I never heard of coax on earphones. Sometimes now I get stuck, and not sure why. My hard drive and processor are wearing out I guess.

It was from a different post. I came here to ask reckless, cause I couldn't find it on google.

And 10-4 on the sales lead.

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#### jlnance

Joined Dec 31, 2015
6
I agree with you, this concept is usually poorly explained. I remember being confused by this when I first learned it because it seems like components had to have a knowledge of the future for this to happen. What is rarely explained is that the 90 degree phase relationship is only true if you're dealing with sine waves. It's the result of the fact that the derivative of a sine wave is another sine wave with a 90 degree phase shift.

You asked about the physics of how this worked. First lets talk about how an inductor works. You have a coil of wire. When a current flows through the wire, it creates a magnetic field around the wire and around the coil as a whole. If the current is constant, this magnetic field does not have much consequence. However, if the current is changing, then you have a coil of wire in a changing magnetic field. A coil of wire in a changing magnetic field will have a voltage induced across it. It doesn't matter if that magnetic field is supplied externally, as it would be in a generator, or supplied by a current flowing through the coil itself, as is the case here.

If you work out the physics, the polarity of the voltage induced across the inductor will be such that it opposes any change in current. It is also proportional to have fast the current is changing.

Here is where the 90 degree phase shift comes from. Assume we have an inductor and we are forcing a sine wave of current to flow through it. The voltage across the inductor at any instant in time is proportional to how fast that sine wave of current is changing. Where does a sine wave change the slowest? At it's maximum and minimum points. So when the current is at it's peak positive or negative value, the voltage across the inductor is 0. Where does a since wave change most rapidly? This turns out to be at the zero crossings of the wave. So when the current is crossing 0, the voltage is at it's maximum or minimum value. If you sketch out what that looks like, it's easy to see the zero crossings and peaks are shifted by 90 degrees from the original wave. If you do the math, it works out to a 90 degree phase shifted shifted sine wave.

For me the important part of understand this was realizing that voltage leading or lagging current doesn't mean the circuit needs to know the future. It's just the result of the fact that for a sine wave, the rate of change of the waveform happens to be another sine wave shifted 90 degrees from the first.

#### DGElder

Joined Apr 3, 2016
351
Sparky, I suspect your problem is that you have not spent enough time learning the fundamental laws of electromagnetics, such as Faraday's law, Coulombs law, Lenz law, the definitions - qualitative and mathematical - for E-fields, H- fields, volts, current, inductance and capacitance, the stored energy in coils and capacitors and their inter-relationships in the context of the conservation of energy. After you develop these insights and vocabulary you will be able to understand their application to the circuit behaviours you are trying to understand or at least ask your questions with more specificity, clarity and less hand waving.

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#### nsaspook

Joined Aug 27, 2009
6,935
You asked about the physics of how this worked. First lets talk about how an inductor works. You have a coil of wire. When a current flows through the wire, it creates a magnetic field around the wire and around the coil as a whole. itself, as is the case here.
Slightly Pedantic.

The word 'creates' here is a bit of a modern physics misnomer. It implies a 'cause and effect' relationship that separates the dynamic (time-varying) electric and magnetic fields into individual objects where one 'creates' the other by charged particles that move a million times slower (drift velocity) in conductors than the fields that surround them. That's not the way we view it normally today. Maxwell unified the Faraday's Law 'a changing magnetic field creates an electric field' and Ampere's Law 'a changing electric field creates a magnetic field' into a unified electromagnetic field with Lorentz force law that explains the interaction of fields with particles that causes it to have the other (electric or magnetic) component suppressed to an observer.

What seems to consist of a "pure" electric or magnetic field, can be converted to an (electromagnetic near-field around the inductor, motors and electrical transformers) EM field, with both E and M components present, by simply moving the observer into the correct frame of reference.

#### BR-549

Joined Sep 22, 2013
4,938
And the reason people think they are separate is because they are perpendicular.

The coil configures and concentrates the existing magnetic field.

#### Tonyr1084

Joined Sep 24, 2015
4,167
I know mine is the 66th post - and it's quite possible someone has already said what I'm about to. And if I should be wrong, I'm sure a LOT of people here will be ready, willing and chomping at the bit to correct me. Be that as it may, this is my limited understanding of why current lags by 90˚ in inductors and leads by 90˚ in a capacitor:

In an inductor, it's the changeing voltage that induces a current. If an inductor is held at a constant potential then there's no change in state and the magnetic flux remains constant. But as the voltage moves from peak (lets say upper peak) to peak (lower peak) then current is at its strongest as the voltage crosses the zero threshold in the sine wave. Current lags by 90˚ because of the changing voltage.

In a capacitor - and I'll use some unconventional terms to describe what (or how I see it) is going on: A capacitor is basically a static storage device. As a voltage rises it first must feed the capacitor. As the capacitor reaches a full state (ignore capacitance and time constants for the moment), as it reaches a full state the voltage begins to rise. The closer to full the faster the rise becomes. In other words, the current must feed the capacitor first BEFORE the voltage can rise. And as the polarity of the sine wave switches (reverses) the capacitor begins to regurgitate its stored charge, thus, before the voltage falls the current rises in the opposite direction.

A very simplistic way of describing it, but that's how I think of it. And I'm SURE LOTS of engineers will be eating me up alive for my analogies. Be that as it may, this is my contribution to this. Even if I'm wrong - if you think of it this way it may help you visualize what's going on. I've always been a "Visual" thinker. I have to see it in my mind to understand it. (and that's why I like books with pictures) And sometimes (often times) there in-lies my inability to grasp some concepts. I'm reading about Boolean Logic today. I got a lot out of it but I still have trouble seeing how things are working. But once I do - that's my "A-HAAA!" moment.

I'll sit quietly and let the sharks begin their feeding frenzy now.

Peace.

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#### WBahn

Joined Mar 31, 2012
25,250
I know mine is the 66th post - and it's quite possible someone has already said what I'm about to. And if I should be wrong, I'm sure a LOT of people here will be ready, willing and chomping at the bit to correct me. Be that as it may, this is my limited understanding of why current lags by 90˚ in inductors and leads by 90˚ in a capacitor:

In an inductor, it's the changeing voltage that induces a current. If an inductor is held at a constant potential then there's no change in state and the magnetic flux remains constant.
Okay, let that be me.

This is simply not true. If you apply any non-zero voltage across an inductor, then it's current will change in response. When we charged a magnet we usually ramped the current using a constant voltage of about 1 V. With a 74 H magnet, that meant that we had to maintain that DC voltage across the inductor for better than three minutes to get it up to the 100 A operating current.

#### Tonyr1084

Joined Sep 24, 2015
4,167
Perhaps I mis-stated my thoughts. If a coil is charged with a DC voltage it will develop a magnetic flux. When you take away that voltage the magnetic field will collapse and induce a voltage back into the circuit. Hence, the need for snubber diodes. And since the question revolves around a sine wave - and a purely sinusoidal wave - then current lags behind the wave form. My comment about holding an inductor charged was intended to state that there is no breakdown in the flux, and thus, no "Lag" in current. But when the voltage is dropped then the current will follow suit. The current will back rush the circuit according to the size of the coil.

Now, you want to talk about a 74 HENRY coil - that's pretty dang big. And I can't imagine what such a large magnet would be used for. Be that as it may, we're not discussing DC voltages applied to coils, we're discussing sine waves. So if my comment was ill represented - that's also why I'm not a technical writer.

Anyone want to debunk what I said about the coil lagging in current because of charge time? I'm open to criticism. If I'm wrong - I can admit it, and I can take in more instruction. So please - if you know how to explain it to me - you have my ear.

#### BR-549

Joined Sep 22, 2013
4,938
This is difficult to explain because is takes several cycles to get to steady state AC.

You can't start off with...."turn the switch on". This has to do with resistance, conductor self inductance and building up flux.

Everyone likes to say current is stored in the flux. nada I think that the flux compresses the increase of current in the coil.

When voltage increases across the coil, instead of following the voltage like it normally would, the current (charge) is compressed and confined in the coil, by the increasing flux field. It is only held and delayed during compression.

Increasing flux compresses, decreasing flux releases, charge. The coil is huffing and puffing charge just like a capacitor does.

Current is inverted in a coil. Rising current goes in.........falling current comes out.

It's just the opposite with a cap. Current shoots straight thru. Rising voltage goes in,......falling voltage comes out.

#### ian field

Joined Oct 27, 2012
6,539
First, you have to apply voltage to the inductor. The inductor refuses to allow current to change instantly because the energy you just applied is being used to create a magnetic field. For any voltage, there is a ramp up of current inversely proportional to the inductance.
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Its probably worth adding the reason why the current ramps up as it adds to the concept of things/events taking a finite time. The current causes lines of magnetic flux to build up around the inductor, as they get more crowded; the current increases.

When you can't cram in any more lines of flux; that's saturation - the coil ceases to be an inductor, and you're left with the DC resistance of the wire its wound with.

#### nsaspook

Joined Aug 27, 2009
6,935
Now, you want to talk about a 74 HENRY coil - that's pretty dang big. And I can't imagine what such a large magnet would be used for. Be that as it may, we're not discussing DC voltages applied to coils, we're discussing sine waves. So if my comment was ill represented - that's also why I'm not a technical writer.
Most people haven't seen or worked on magnetic beam deflection systems where the magnetic flux changes from ramp step to ramp stop is measured in seconds. The really old machines used large electromagnets to scan the beam across the wafers at 24vdc and up to 200A.

At each instant in time to the next it makes little difference to the inductors magnetic flux if it's DC step or a sine wave that caused the rate of change in the magnetic field.

#### DGElder

Joined Apr 3, 2016
351
Magnetic Flux is not a change in magnetic field. His first equation, which is correct, contradicts his first statement.

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#### BR-549

Joined Sep 22, 2013
4,938
I don't think we are aware of the power and importance of the magnetic.

The potential of the electric is from charge separation. We can sub-stain that separation.

But the potential of the magnetic comes from charge acceleration. We can not sub-stain that.

The electrons suffer billions of collisions to move forward. Every collision is almost a stop. This is the only reason we can have steady current.

If we remove the collisions (resistance) , the only thing opposing acceleration is self inductance.

That's ok, because that will only add duration (delay not stoppage) to the full magnetic potential.

Now we should experience what the real magnetic field around a conductor acts like.

Very strong and shielding. And I would advise against using a knife switch. Big time kick back.

True magneto power.

But even more important. Gravity only accumulates. The magnetic binds particles into matter.

#### johnmariow

Joined May 4, 2016
20
You know a lot more than you think you do. This brick wall is pretty common because you don't yet have the proper geometric theory in your head. You can keep banging at the circuit equations with the help of phasor diagrams until you can do them in your sleep and finally understand what they mean or you can step back a bit and examine Electromechanics a bit as 4-D spacetime (space and time) fields to understand what we commonly think of the separate (electric) voltage and (magnetic) current elements are really different views of one dual-entity EM field.

This won't likely help with your present questions about EMF but it might open a new vista on how to interpret your studies.

Excellent explanation. The graph with the voltage sine wave and the current sine wave clearly shows the voltage leading the current. And this is probably the only way one can conceptualize it; i.e. in terms of sine functions.

You know a lot more than you think you do. This brick wall is pretty common because you don't yet have the proper geometric theory in your head. You can keep banging at the circuit equations with the help of phasor diagrams until you can do them in your sleep and finally understand what they mean or you can step back a bit and examine Electromechanics a bit as 4-D spacetime (space and time) fields to understand what we commonly think of the separate (electric) voltage and (magnetic) current elements are really different views of one dual-entity EM field.

This won't likely help with your present questions about EMF but it might open a new vista on how to interpret your studies.

So when we see the voltage current waveform in a purely inductive circuit you can note the relationship between the rapid rate of change of the charges at the zero crossing matches to the peaks of current (magnetic field) while the slow rates of change at the voltage peaks matches current (magnetic field) nulls. A changing magnetic fields give rise to a changing opposing electric field that limits the current. The energy of this circuit is in the fields not the charge carrier electrons (current) so the stored EM energy in the inductor is just sloshing back and forth instead of being dissipated.

Simple harmonic motion

How we view this (EM energy as electric or magnetic) depends on the 'projection' we see as it moves in space and time.

http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=guide_dft_projection_circular_motion

So when we see the voltage current waveform in a purely inductive circuit you can note the relationship between the rapid rate of change of the charges at the zero crossing matches to the peaks of current (magnetic field) while the slow rates of change at the voltage peaks matches current (magnetic field) nulls. A changing magnetic fields give rise to a changing opposing electric field that limits the current. The energy of this circuit is in the fields not the charge carrier electrons (current) so the stored EM energy in the inductor is just sloshing back and forth instead of being dissipated.

Simple harmonic motion

How we view this (EM energy as electric or magnetic) depends on the 'projection' we see as it moves in space and time.

http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=guide_dft_projection_circular_motion

#### recklessrog

Joined May 23, 2013
985
View attachment 105804 This is a little device I built a few years ago primarily for testing the saturation point of unknown inductors. The top trace is the pulse that is applied to the component under test and the bottom trace is the current through the inductor over time. It clearly shows that the applied voltage is a very fast rising square wave and the current increases fairly linearly until the core starts to saturate whereupon the current rises sharply.
In the context of this thread, it shows that the current lags the voltage, but can also be used to determine the inductance etc although I have a Peak L.C.R tester that can show many more characteristics but does not test the saturation.
I have re-loaded this as for some reason the txt disappeared, probably my fault when I uploaded better pictures.

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#### recklessrog

Joined May 23, 2013
985
This is the Peak L.C.R 45, really is very good!

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