# HOW does voltage lead current in an inductive circuit?

#### Sparky82

Joined May 1, 2016
2
Hello. Thanks in advance for anyone able to provide clarity to my questions.

I'm desperately trying to making sense of PHASE SHIFT.
I've read statement after statement regarding the description of how voltage leads current in an inductive circuit, and how current leads voltage in an inductive circuit ; however, every statement leaves a lot of open ends through lack of description due to specifics and/or not using practical visuals.

Yes, I can interpret a sine chart showing the 90 degree phase displacements and how at peak X we have zero value Y...that's wonderful and all; however, HOW is that happening in the real world before math is used to describe it?!?!
Does the 90 degree flux line from a coiled conductor cut back on itself, essentially imposing a self-manifested wall on source current but voltage is still able to truck on by unfettered? Wtf?

A textbooks typical description is typically something like "an inductor opposes the change in current...blah-blah-blah" Oh? Is that a current change that's increasing or decreasing at the same time the flux is doing X? Is the back emf of the collapsing mag flux pushing source voltage back FROM the supply or TO the supply? Is the "voltage" that's leading an "EMF" voltage or Potential Difference voltage or Resultant Voltage or Apple-Pie in the Sky voltage?!?!
Like, Jesus Christ, why is this so hard to get a clear answer to? Literally hundreds of sources repeating the same garb.

I'd be forever appreciative if someone can set the record straight and provide some explicitly concise detail and visuals.

Links to suggested sources are appreciated and will be combed over.

Thanks

#### Papabravo

Joined Feb 24, 2006
12,853
Sorry man. AFAIK there is no hand waving "magic bullet" explanation that will satisfy you. Either you understand what is happening or you don't. If it is any consolation to you I didn't understand it either the first time I came across it. I kept reading and experimenting and nipping around the edges and it came upon me suddenly. If this stuff was easy then everybody could do it and salaries for degreed EE's would plummet. Oh....wait.....my bad, that is exactly what has happened. I guess it is not as tough as I thought. Either that or employers no longer care.

If you reject and cannot understand the precise formulation that leads to the insight then I fear there is no helping you. By all means let everybody try, but I fear it is a fool's errand.

#### Sparky82

Joined May 1, 2016
2
Sorry man. AFAIK there is no hand waving "magic bullet" explanation that will satisfy you. Either you understand what is happening or you don't. If it is any consolation to you I didn't understand it either the first time I came across it. I kept reading and experimenting and nipping around the edges and it came upon me suddenly. If this stuff was easy then everybody could do it and salaries for degreed EE's would plummet. Oh....wait.....my bad, that is exactly what has happened. I guess it is not as tough as I thought. Either that or employers no longer care.
Well, I appreciate the laugh, that's for sure.
I just find it funny that the world electrical community that prides itself on "reason and clarity" is anything but....at least the scribes aren't.

I'm not a hapless student, I've received honours in previous studies and am top-of-class with electrical studies....along with continually stumping my profs, I'm just fed up that you can get so far and know very little; it simply won't do.

(Minor edit by moderator)

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#### #12

Joined Nov 30, 2010
18,190
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. In steady flow, the magnet field just stands there and the impedance seems to be the ohmic resistance of the wire that was used to make the inductor. When you try to open the circuit, the magnetic field collapses and its energy wants to keep the current flowing the same way it was already flowing.

With a capacitor, it's like a bucket. You have to pour current into it before the voltage rises. Current leads voltage.
With an inductor, you have to apply voltage and wait for the current to increase. Voltage leads current.

#### WBahn

Joined Mar 31, 2012
25,217
Hello. Thanks in advance for anyone able to provide clarity to my questions.

I'm desperately trying to making sense of PHASE SHIFT.
I've read statement after statement regarding the description of how voltage leads current in an inductive circuit, and how current leads voltage in an inductive circuit ; however, every statement leaves a lot of open ends through lack of description due to specifics and/or not using practical visuals.

Yes, I can interpret a sine chart showing the 90 degree phase displacements and how at peak X we have zero value Y...that's wonderful and all; however, HOW is that happening in the real world before math is used to describe it?!?!
Does the 90 degree flux line from a coiled conductor cut back on itself, essentially imposing a self-manifested wall on source current but voltage is still able to truck on by unfettered? Wtf?

A textbooks typical description is typically something like "an inductor opposes the change in current...blah-blah-blah" Oh? Is that a current change that's increasing or decreasing at the same time the flux is doing X? Is the back emf of the collapsing mag flux pushing source voltage back FROM the supply or TO the supply? Is the "voltage" that's leading an "EMF" voltage or Potential Difference voltage or Resultant Voltage or Apple-Pie in the Sky voltage?!?!
Like, Jesus Christ, why is this so hard to get a clear answer to? Literally hundreds of sources repeating the same garb.

I'd be forever appreciative if someone can set the record straight and provide some explicitly concise detail and visuals.

Links to suggested sources are appreciated and will be combed over.

Thanks
Hate to break it to you, but that math "garb" that you want to avoid IS the language of physics and, as a consequence, electronics. There is only so much understanding you can achieve without understanding the math that describes it.

By the definition of inductance, the voltage across an inductor and the current through an inductor are related by the following constitutive relation:

$$V_L \; = \; L \frac{dI_L}{dt}$$

If the current is sinusoidal then take the derivative and you will see that the voltage will be a sinusoid that leads that current by ninety degrees. A similar, but opposite, relationship holds for a capacitor.

To look more closely as some of your questions:

A textbooks typical description is typically something like "an inductor opposes the change in current...blah-blah-blah" Oh? Is that a current change that's increasing or decreasing at the same time the flux is doing X? Is the back emf of the collapsing mag flux pushing source voltage back FROM the supply or TO the supply? Is the "voltage" that's leading an "EMF" voltage or Potential Difference voltage or Resultant Voltage or Apple-Pie in the Sky voltage?!?!
Like, Jesus Christ, why is this so hard to get a clear answer to? Literally hundreds of sources repeating the same garb.
Yes, an inductor produces a voltage across it that opposes any change in the current through it. If you try to lower the current, the induced voltage will be of a polarity that would attempt to increase the current, while if you try to increase the current the induced voltage will be of a polarity that would attempt to decrease the current. This is a direct consequence of the fact that the current in the inductor produces a magnetic flux through the coil. When you try to change the flux (by changing the current), the changing flux produces a voltage across those same coil windings. If the flux is increasing the voltage is one polarity and if the flux is decreasing the voltage is the opposite polarity. That the induced voltage tends to oppose the change in flux that is producing it is captured by Lenz's Law (which, like most "laws" of this type are merely mathematical descriptions of observed phenomena).

Many of the phrases you are using make little sense. You don't "push source voltage back" either from or to the supply. The induced voltage appears as a voltage difference across the inductor.

#### Papabravo

Joined Feb 24, 2006
12,853
I'm tempted to give odds on the insufficiency of those answers, as excellent as they are.

#### crutschow

Joined Mar 14, 2008
24,295
First thing to note is that inductors store energy in their inductance.
The analog of this in the mechanical world is the inertia of a mass.
If you apply a force (voltage) to a mass (inductance) then it will slowly pick up velocity (current).
The rate of this increase is directly proportional to the force (voltage) and inversely proportional to the mass (inductance).
The velocity of the mass (current in the inductance) stores energy (1/2 mV² for mass and 1/2 LI² for inductance).
Now if you remove the force (voltage) this stored energy will tend to keep the mass (current) moving.
Even if you now reversed the applied force (voltage) the mass (current) will still want to keep moving in the same direction, but slowing down until all the energy has dissipated.

If the force (voltage) is periodically applied and reversed in a sinusoidal fashion then the system will settle into a steady-state oscillation where the velocity (current) will be such that it keeps increasing in the forward direction until the forward force (voltage) returns to zero, at which time the velocity (current) will have reached its peak value.
This is true because the velocity (current) keeps increasing as long as there is any value of force (voltage) being applied.
Similarly the velocity (current) reaches a peak in the reverse direction when the reverse force (voltage) again returns to zero.
This means the velocity (current) always lags the force (voltage) by 90°.

Does that help make sense of it for you?

#### wayneh

Joined Sep 9, 2010
16,228
FWIW, I never got it until I became very comfortable with the calculus and differential equations describing it all. I had math first and actually learned it well enough that I still use it decades later. Then when I encountered electronics, I could just "see" it all in terms that made sense. I frankly can't imagine having any feel for it at all without that solid foundation of math. For me, knowing the math first made it like having F=ma and then deriving the laws of motion. It's easy. But trying to just remember or intuit them is impossible.

#### Papabravo

Joined Feb 24, 2006
12,853
If anybody thinks classical mechanics is tough to understand without the mathematics, then quantum mechanics and general relativity will positively blow you to Bermuda!

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#### wayneh

Joined Sep 9, 2010
16,228
I aced P-chem (quantum mechanics) but I feel like I learned less in that class, with more pain, than any other class I took in college.

#### jpanhalt

Joined Jan 18, 2008
8,711

#### nsaspook

Joined Aug 27, 2009
6,885
Well, I appreciate the laugh, that's for sure.
I just find it funny that the world electrical community that prides itself on "reason and clarity" is anything but....at least the scribes aren't.

I'm not a hapless student, I've received honours in previous studies and am top-of-class with electrical studies....along with continually stumping my profs, I'm just fed up that you can get so far and know dick-shit; it simply won't do.
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

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#### crutschow

Joined Mar 14, 2008
24,295
FWIW, I never got it until I became very comfortable with the calculus and differential equations describing it all. I had math first and actually learned it well enough that I still use it decades later. Then when I encountered electronics, I could just "see" it all in terms that made sense. I frankly can't imagine having any feel for it at all without that solid foundation of math. For me, knowing the math first made it like having F=ma and then deriving the laws of motion. It's easy. But trying to just remember or intuit them is impossible.
I really admire anyone who can "see" in mathematical terms.
I can't. I'm a visual guy and math is not visual to me.
I learned all the differential equations describing circuit behavior and can use them when necessary but they do little to help my comprehension of the circuit operation. For that I need to have (for lack of a better term) an intuitive feel for what's happening. The math is there to help me quantify the circuit operation, but that's it.

For example, I had little real understanding of how an inductor works based upon the inductive magnetic field equations. It was sort of black magic until I came upon the inertia analogy. Then it became very clear to me how inductors work. For example it was then easy to see why inductive voltage spikes occur and the correct polarity of those spikes, no math needed.
(I've seen a number of people on these forums mangle that nature of that effect by their misinterpretation of the equations.)
The analogy also made it easy for me to see how an LC oscillation is simply the periodic transfer of energy back and forth between the capacitor voltage electric field and the inductive current magnetic field.

#### recklessrog

Joined May 23, 2013
985
I really admire anyone who can "see" in mathematical terms.
I can't. I'm a visual guy and math is not visual to me
I was trying to explain how a moving magnetic field in a coil induced a voltage in a coil that could produce a magnetic force.
No mater how I drew it or explained it, one guy couldn't get it.
To show him in a "real physical way" I got a 12" length of plumbers copper pipe, a rare earth high power button magnet and dropped it down the tube. There was look of sheer amazement on the face of the guy as he saw that it dropped 12" through the tube slower than in free air. He then grasped the principle that the moving magnet induced an electric current in the copper tube that in turn created a magnetic field that opposed the movement of the magnet thereby slowing it's decent. Then we applied the maths which he fully comprehended having seen it in action .

#### BR-549

Joined Sep 22, 2013
4,938
Math is the BANE of understanding. No one should be taught math until after graduating.

You can not "reverse engineer a equation" to determine process or cause.

This is what modern science does. This is why they teach the fallacy of the standard model for 100 years. To satisfy an equation.

If math is useful as experimental tool..................why after 100 years, why can't modern science tell me what an electron is, what is looks like, and how does it physically change energy level?

Yeah right.....................math clears everything up.

Cause and process will give you the right math.

But the math will not give you the right process.

Electrons do NOT orbit protons. Silly silly math.

#### hp1729

Joined Nov 23, 2015
2,304
Hello. Thanks in advance for anyone able to provide clarity to my questions.

I'm desperately trying to making sense of PHASE SHIFT.
I've read statement after statement regarding the description of how voltage leads current in an inductive circuit, and how current leads voltage in an inductive circuit ; however, every statement leaves a lot of open ends through lack of description due to specifics and/or not using practical visuals.

Yes, I can interpret a sine chart showing the 90 degree phase displacements and how at peak X we have zero value Y...that's wonderful and all; however, HOW is that happening in the real world before math is used to describe it?!?!
Does the 90 degree flux line from a coiled conductor cut back on itself, essentially imposing a self-manifested wall on source current but voltage is still able to truck on by unfettered? Wtf?

A textbooks typical description is typically something like "an inductor opposes the change in current...blah-blah-blah" Oh? Is that a current change that's increasing or decreasing at the same time the flux is doing X? Is the back emf of the collapsing mag flux pushing source voltage back FROM the supply or TO the supply? Is the "voltage" that's leading an "EMF" voltage or Potential Difference voltage or Resultant Voltage or Apple-Pie in the Sky voltage?!?!
Like, Jesus Christ, why is this so hard to get a clear answer to? Literally hundreds of sources repeating the same garb.

I'd be forever appreciative if someone can set the record straight and provide some explicitly concise detail and visuals.

Links to suggested sources are appreciated and will be combed over.

Thanks
No math required. As current starts to flow a magnetic field starts to build up around each wire in the coil. The expanding magnetic field crosses other wires inducing a current in the opposite direction. So current flow is inhibited but not the voltage.

#### WBahn

Joined Mar 31, 2012
25,217
I aced P-chem (quantum mechanics) but I feel like I learned less in that class, with more pain, than any other class I took in college.
For me it was statistical thermodynamics. The professor walked into class the first day and threw two six-sided die on the table and asked what was the probability of rolling a seven. We figured it out and told him and then he said, "From these humble beginnings we will hence forth derive all of classical thermodynamics." And then he spent the entire semester doing precisely that! It was interesting and fascinating and I walked away with virtually nothing useful actually learned (but I'm still glad I took it and sometime I wouldn't mind retaking it because I think I am in a much better position to appreciate the subtle details that went sailing past me before).

#### WBahn

Joined Mar 31, 2012
25,217
I really admire anyone who can "see" in mathematical terms.
I can't. I'm a visual guy and math is not visual to me.
Same here. I can sometimes get glimpses into the mathematical world, but usually have to make an effort to map the mathematical ramifications into a world in which I can visualize a reasonable analogy. I have a colleague that CAN think purely in terms of the math -- and he does the opposite in that he makes an effort to map what he sees into mathematical terms and relationships. He is scary brilliant and both a lot of fun and a bit intimidating to work with. Fortunately my strengths offset some of his few weaknesses, so while I am definitely the junior member of the team, we make a remarkably good team, each finding things that the other missed.

#### wayneh

Joined Sep 9, 2010
16,228
...(but I'm still glad I took it and sometime I wouldn't mind retaking it because I think I am in a much better position to appreciate the subtle details that went sailing past me before).
I feel that way about many of my college classes, but most assuredly NOT quantum mechanics.

I don't think I'm particularly gifted in math. My advantage was getting exposed to calculus in high school and then having a very rigorous and advanced calculus class my first semester of college. After that, it was easy to internalize anything that came later in physics and science classes. When vectors were introduced in Physics, most of my fellows were blown away and struggling. It was trivial to me and even felt dumbed-down. I was able to think about the actual physics involved and didn't have to waste brainpower on scalars and vectors and cross products.

None of that helped in P.Chem. I'd never seen most of the math that gets used in P.Chem and I suffered along with everybody else.

#### WBahn

Joined Mar 31, 2012
25,217
I don't recall my P-chem class involving quantum mechanics, but I took it as a first semester freshman and was quite unprepared for the math. I was taking Calc II at the same time and also Physics I. It was the first time that I had dealt with partial derivatives and most of my effort was struggling with the mechanics and I wasn't able to focus on the concepts. It's very possible that the material was straight out of quantum mechanics and that either it wasn't presented in that vein or I wasn't in a position to appreciate it. When I hit quantum later in my physics curriculum I was much better prepared for it.

But I sure agree that having a solid math understanding makes it SO much easier to learn and actually comprehend any subject that uses that math -- and that the reverse is also very true in that if you have to fight the math, you will have a much harder time understanding the concepts involved in the subject you are studying.

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