How to understand an inductor?

[Hanalee]

Good day, all
I'm having a hard time visualizing what is happening in an inductor and why it is happening. I understand the graphs and practical application from Why Use Inductors in Circuit? but I can't seem to physically understand what is happening as you pass current through the inductor besides the fact that it builds a magnetic field. I think the relationship between the magnetic field and the circuit is confusing me.

If anyone could help me with a basic explanation of why an inductor resists change to current it would be greatly appreciated.

 

[__dan]

E = L di/dt.

I scrolled through your link quickly but nowhere did I see this.

E is Voltage drop across the inductor, L is a fixed constant for inductance due to the construction of the element device, di / dt is typically a sinewave but in a practical sense represents the instantaneous rate of change of current (di) with time (dt).

For a fast changing current with time, either high frequency sinewave or transient impulse, the inductor will tend to drop Voltage across it rather than pass current. Big di/dt, times the constant L, gives big E Voltage drop across the inductor.

For a current that does not change with time, steady state DC, di / dt is zero, times the fixed constant L, gives zero for voltage drop across the inductor. It is a short for DC but drops Voltage across it for non zero di / dt, proportional to the inductance L.

The inductor is lossless and will store energy in the magnetic field as it charges, giving it all back when it discharges. Again the relation is E = L di / dt. So when an inductor suddenly goes open circuit and the di / dt is changing very rapidly, times the inductance L, gives a very high E open circuit instantaneous High Voltage kick.

 

[junkhound]

Is the dc or ac the part that bothers you? will put in terms of current since that is the main term u used.
dc: the higher the current, the more flux (think of as lines if need be) generated. Magnetic materials only have so many little dipoles, once they are all aligned it is called saturation and no further rise in current can increase the flux. There is no limit on how much flux can be created in air or a vacuum.

ac: now turn the current in opposite direction. As the current increases, flux rises, reverses and flux builds in the other direction. The faster this goes, the less time on each cycle the flux has to build. Basic equation is integral V*dt = NBA in voltage terms for flux (A = core area, not amps). You can calculate current then knowing that relationship.

 

[Hanalee]

Thank you for sharing ideas.
My thought from basic inductor differential equation and all you replies

The voltage across an inductor is related to the change in the current through the inductor. This helps to explain the phase shift in voltage across inductors in circuit analysis problems, and also helps to understand the kickback voltage that is generated when open a circuit that has an inductor carrying a current through it.

 

[Fred B]

Thank you for sharing ideas.
My thought from basic inductor differential equation and all you replies
View attachment 2557191
The voltage across an inductor is related to the change in the current through the inductor. This helps to explain the phase shift in voltage across inductors in circuit analysis problems, and also helps to understand the kickback voltage that is generated when open a circuit that has an inductor carrying a current through it.

Kickback voltage? Sorry if stupid question, could you please explain what it is and the process.

 

[GoldDigger]

A basic observation that may help your understanding is called Lenz's Law.
It states that when a current is induced in a circuit by a changing magnetic field, the magnetic field produced by that induced current will oppose the change in magnetic field that caused it.
It does not give you the magnitude. That has to come from the basic inductor equation which in turn comes from Maxwell's Laws of Electricity and Magnetism. But if you, like me, always have trouble keeping signs straight, it "points you in the right direction."

 

[Fred B]

A basic observation that may help your understanding is called Lenz's Law.
It states that when a current is induced in a circuit by a changing magnetic field, the magnetic field produced by that induced current will oppose the change in magnetic field that caused it.
It does not give you the magnitude. That has to come from the basic inductor equation which in turn comes from Maxwell's Laws of Electricity and Magnetism. But if you, like me, always have trouble keeping signs straight, it "points you in the right direction."

Is this what causes wire on higher voltage to "jump" when shutting down? Is it similar to water hammer that sometimes can get when you shut down water flow rapidly?

 

[GoldDigger]

Is this what causes wire on higher voltage to "jump" when shutting down? Is it similar to water hammer that sometimes can get when you shut down water flow rapidly?

Absolutely. The sudden decrease in the magnetic field tries to induce a current which counteracts the change. Which in turn leads to a potentially high voltage. The water hammer analogy is, IMO, a good one for understanding.

Energy is stored in the magnetic field and somehow work has to be done to dissipate that energy.

 

[Fred B]

Absolutely. The sudden decrease in the magnetic field tries to induce a current which counteracts the change. Which in turn leads to a potentially high voltage. The water hammer analogy is, IMO, a good one for understanding.

Energy is stored in the magnetic field and somehow work has to be done to dissipate that energy.

I knew that motor loads can cause a reverse feed back when it is shut down, didn't realize an inductor could cause and issue. If my understanding is correct an example of an inductor would be a heating element? Is there a safety concern with kickback voltage or just neusence?

 

[winnie]

My hand waving approach:

Current flowing in a wire creates a magnetic field. DC current means steady (DC) field.

A changing magnetic field creates a voltage in a wire.

When you apply a voltage to a wire, it causes the current in that wire to change. The changing current means the wire is in a changing magnetic field that it is itself creating. This changing magnetic field creates a voltage.

-Jon

 

[winnie]

I knew that motor loads can cause a reverse feed back when it is shut down, didn't realize an inductor could cause and issue. If my understanding is correct an example of an inductor would be a heating element? Is there a safety concern with kickback voltage or just neusence?

The inductance of a heating element is pretty small, and generally negligible for 60 Hz circuits.

The common electrical situation where inductive kick is a problem is DC solenoids. Often a diode is used to protect switch contacts from the arc caused by the inductance trying to maintain current flow.

Jon

 

[Besoeker3]

e=-Ldi/dt?

 

[GoldDigger]

e=-Ldi/dt?

Sounds like a winner to me. Although different people have different choices for capitalization.

See post #2

 

[Besoeker3]

Sounds like a winner to me. Although different people have different choices for capitalization.

But this is the right one.............................

 

[paulengr]

I just think of it like this. Imagine you have a long wire. Now coil it up so it doesn’t take as much space. It causes the current to have a little time delay in it. So the current lags the voltage. The real world has a magnetic field that builds up and collapses. With filters inductors resist rapid changes in current but not voltage. So it passes DC but blocks RF for instance.

 

[__dan]

Edit to add.

Instead of saying it is energy stored in a field, a phrase I came across that I liked better is

in the general case, it is a displacement in a field subject to a restoring force (Sawyer).

It makes for a much more interesting picture of what may be happening.

How it actually does this, in the sense of the underlying physical reality that we only try to describe mathematically, I don't know if anyone has a clue. Lines of force, stored energy, are just thought pictures to aid conceptual investigation process (this could be a pretty good thread).

You know, why does the displacement need to be restored, and then must be done violently and in that instant, in the case of the inductor going instantly open circuit.

 

[GoldDigger]

Edit to add.
...

You know, why does the displacement need to be restored, and then must be done violently and in that instant, in the case of the inductor going instantly open circuit.

Which is why, in the real world, any inductor that is able go open instantaneously also has some capacitance in parallel with the inductor.

 

[xptpcrewx]

Good day, all
I'm having a hard time visualizing what is happening in an inductor and why it is happening. I understand the graphs and practical application from Why Use Inductors in Circuit? but I can't seem to physically understand what is happening as you pass current through the inductor besides the fact that it builds a magnetic field. I think the relationship between the magnetic field and the circuit is confusing me.

If anyone could help me with a basic explanation of why an inductor resists change to current it would be greatly appreciated.

I'll try my best, but first I need to set this up a bit by talking about inductance:

1. We know a single wire conducting a current exhibits a circular magnetic field around this current which emanates radially outward into space. The magnetic field encircling this current also exists everywhere continuously along the length of the wire.​

​

The internal flux associated with this current is a function of how much magnetic field exists within the conductor. It can be thought of as the product of the length and summation of magnetic fields for each infinitesimal filament of current starting from the center out to the radius of the conductor.​

​

The external flux associated with this current is a function of how far the magnetic field extends out into the universe. It can be thought of as the product of the length and summation of the magnetic fields starting from the radius of the conductor out to an infinite distance perpendicular to the current.​

​

Note: The internal + external flux per ampere is the inductance of the wire. Also referred to as the total inductance. This physical/geometry dependent property is a description of how much flux is generated for a given current; or a measure of how much magnetic energy is stored in a component/arrangement/system. Each current filament has its own self-inductance and each pair of current filaments has a mutual inductance.​

​

2. If the wire described above is bent 90 degrees, then the circular magnetic fields along the length of the wire can be thought of as becoming more compressed everywhere on the inside corner. This bend also causes the magnetic fields to intersect with the internal flux as it is acting in parallel or perpendicular to the wire. As you can imagine, this increases the total self- and mutual inductances of the system (as there is now more total flux per ampere).​

​

3. Extending the above analogy - Instead of a sharp 90-degree bend, consider a gradual curve such that one circular loop is formed. Due to the geometry of the current loop, the magnetic fields are further compressed into a confined area (encircled by the loop). Although the magnetic field still extends everywhere into space (like in the previous examples), they are now cancelled everywhere outside the loop, but concentrated/condensed/reinforced in the center. Depending on how wide this loop is, dictates how much flux is generated for a given current. Add more loops/turns and this increases the total self- and mutual inductance (as more flux per ampere is generated).​

Items 1, 2, and 3 above describe how a current establishes a magnetic field and how the physical geometry can affect the flux. At this point, you may ask why is it important to understand flux for visualizing how an inductor works? It's because for the above cases, structural changes in topology causes the magnetic fields to intersect and interact more with the internal and/or external fluxes such that they are more effectively linked to the current. More flux linkages means the system it is more efficient in generating flux, and consequently, easier for these magnetic-field intersections/interactions to induce opposing currents back into the system.

By Faraday/Lenz's law, when you excite a closed loop with time-varying fields, a corresponding change in current tries to happen... which is the same thing as trying to change the magnetic flux encircled by that loop… which simultaneously causes a portion of the intersecting/self-interacting flux to push back... which is ultimately the same thing as a current going in the opposite direction. This is really nothing other than opposition to current flow. More precisely, its an opposition to the rate of change of current (as the flux must be time-varying for any opposition to occur). As an exercise, try to visualize how these changing fluxes induce circulating eddy currents which partially cancel or reinforce the individual current filaments internal to the wire. Overall, there are two fields – one having to do with the forcing action as a result of excitation, and the other having to do with the reaction or counter-EMF.

Sorry that was long. I hope it helps…

 

[Hanalee]

Thank you all again
My thought...

di/dt is the change in current per unit time. When a current goes through an inductor it creates a magnetic field. YI just need to accept that or watch some feynman physics lectures (well, youtube might have some videos, too) Creating that field required energy. When initially apply voltage to an inductor, initially there is no field. The current slowly starts ramping up as the field is created. (di/dt is created by V based on the inductor size) The formation of the field resists (slows, or impedes) the growing current. An ideal inductor has no ohmic resistance so the current, and the field, can grow forever for any given V. If I stop the current from growing (which, strangely enough, leaves zero voltage across the inductor since di/dt is zero), the field is simply maintained. If I reduce the current, the field collapses some while trying to keep the current the same (and a voltage results).

So the basic action of an inductor is that it resists current changes through stored energy in its magnetic field. Increasing current is resisted by the growing field, decreasing current is resisted by the collapsing field. If I stop the current altogether, I get a huge voltage as the field collapses and creates an infinite voltage to try to maintain the field.

v(t)=L di(t)dt basically means that applying a constant voltage causes a constant ramp in current (regulated by the increasing magnetic field).

To say it another way, the creation of a magnetic field induces current that impedes the growth of the field. The field changes cutting across the wires always resists the current that is creating or collapsing the field.

According to Lenz's law the direction of induced e.m.f is always such that it opposes the change in current that created it.

 

[synchro]

I agree with your observations and thoughts.

... An ideal inductor has no ohmic resistance so the current, and the field, can grow forever for any given V. If I stop the current from growing (which, strangely enough, leaves zero voltage across the inductor since di/dt is zero), the field is simply maintained.

Superconducting electromagnets inside MRI machines in hospitals, particle accelerators, etc. are like the ideal inductor you describe, although they have a current limit above which they will "quench" and no longer be superconducting. The current in such a superconducting coil is built up slowly with a power supply to the design value, and then a shunt across the coil input is allowed to become superconducting itself to create a zero resistance short circuit across the coil. The current in the coil will then continue to circulate and maintain the magnetic field, typically for several days to months at a time without any applied input current.

You mentioned that "v(t)=L di(t)/dt basically means that applying a constant voltage causes a constant ramp in current (regulated by the increasing magnetic field)."
Another useful way of looking at this is to take V(t)=L dI(t)/dt and integrate both sides of the equation.
You get: I(t) = 1/L ∫ V(t) dt + I₀
Then I think it's more obvious how the current will build up or decay as a function of any arbitrary applied voltage waveform V(t) . The instantaneous current I(t) will just be the area under the V(t) waveform in volt-seconds, plus an initial current I₀ if there is one. The integral of a voltage step is a ramp, the integral of a triangle wave is a parabolic one, etc.
By the way, the stored energy will be 1/2 L I²(t) .