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Need help understanding inductors

  1. Aug 29, 2015 #1
    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 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.
  2. jcsd
  3. Aug 29, 2015 #2


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    Welcome to the PF, Curious.

    At least for me, the basic inductor differential equation has helped me the most to feeling comfortable using them:

    [tex]v(t) = L \frac{di(t)}{dt}[/tex]

    So 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 you open a circuit that has an inductor carrying a current through it.
  4. Aug 29, 2015 #3


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    This interactive image from the HyperPhysics website may give you ways to visualize the differential equation that berkeman provided and the physics behind it.

  5. Aug 30, 2015 #4


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    di/dt is the change in current per unit time. It is key to understanding inductors.

    When a current goes through an inductor it creates a magnetic field. You just need to accept that or watch some feynman physics lectures (well, youtube might have some videos, too) Creating that field required energy. When you 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.
  6. Aug 30, 2015 #5
    Its important to get the terminology correct in the case of inductors.

    Ideal inductors don't resist change in current; they oppose a change which is a crucial difference.

    The total opposition to current in an AC circuit is impedance, or which resistance is just a part. Of course, in reality, all components have a resistive element, but this is a different process, and its important not to confuse the two, because very different results arise.
  7. Aug 30, 2015 #6


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    Inductor stores energy in magnetic form. When you apply step voltage to an RL circuit, inductor acts as an open switch at that instant, causing all the voltage to drop across it. It opposes the applied voltage till the rate of change of current is 0 (almost), which depends on the time constant L/R. This behavior is best explained with a differential equation that you already know. As the current builds up, energy gets stored in the inductor and it finally becomes LI2/2 at the steady state. If you removed L from the circuit, the steady state would appear instantly after applying the voltage. But with inductor, it takes some time (in which the inductor stores energy) to reach the same steady state condition.
  8. Aug 30, 2015 #7

    jim hardy

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    Charge in motion is current
    but unlike matter in motion, charge has no mass to establish inertia.

    There's a quaint property of the universe that surrounds charge in motion with a magnetic field,
    and that's where charge in motion stores its "inertia".

    Mass in motion has kinetic energy ½ M v2
    Charge in motion has energy (Kinetic or Potential? i'm unsure) ½ L I2
    where L is inductance of the circuit, amount of magnetic flux per amp.
    We can physically arrange the circuit to maximize inductance.

    so what goes on in an inductor is: electrical energy is moved from the source into the magnetic field, to be returned at some later time.

    magnetic field around a wire , courtesy http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html


    arranging the circuit for more inductance

    any help ?

    old jim
  9. Sep 2, 2015 #8


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    Note to participants: please reserve inclusion of losses for another thread.

    The goal in the present discussion is towards an understanding of pure inductance as a circuit element.
  10. Sep 2, 2015 #9

    jim hardy

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    It was observed before it was figured out. Look up Lenz's law.


    Here is a simplistic explanation at the nuts & bolts level.

    In this inductor, should current try to change because of something somebody did out there in the external circuit,
    the magnetic field must grow or shrink.
    As it does, the magnetic lines move outward or inward. As they cross the conductors they apply force to free charges inside the conductors. You do believe in QV cross B ?
    Those forces, integrated along the length of the wire, make a voltage at the inductor's terminals that opposes the change in current.
    (Search on Lenz's Law).

    Now as you know, rate of change is slope on a graph ,
    and rate of change of current of current is di/dt,
    and the voltage across an inductor is L * di/dt

    Sinusoids don't change shape when you differentiate them so it's not apparent by looking at them this derivative exists, all you see is phase shift.

    Here's an actual 'scope photo of volts across an inductor with a triangle wave current

    current above, ~20 ma p-p
    voltage below , somewhat less than a volt p-p

    Triangle wave current has two distinct slopes
    and (almost) square voltage wave has two distinct levels,
    which to me is visual proof e = L di/dt.
    (Rounded corners of squarewave are a secondary effect from imperfect iron core in this inductor. They weren't there with air core.)

    The inductor does its best to keep current constant.

    Same exact reason a flywheel resists change in rotation. Energy is conserved. Magnetic of the inductor field stores it .

    There's probably an electrical analogy to gyroscopic properties of a flywheel too, but my vector calculus is too weak to explore that thought.

    Any help? When your mind will work it like inertia, the formulas become intuitive.
    Surely you've spun motors by hand and felt their inertia. The work you put in with your hand comes back out as force opposing your hand, not as heat. Energy is stored in the inertia for return later. Just like an inductor.

    I oversimplify this way to help you over the same stumbling blocks i struggled past.
    Work those differential equations and refine your mental model until the math flows naturally from it. That sure beats cramming for exams...

    old jim
  11. Sep 2, 2015 #10


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    If it helps - I can offer another "analogy", which is even more than an anlogy:
    We can replace the energy of the magnetic field by the energy of the E-field of a capacitor.

    The background is as follows: There is an active electronic circuit involving two opamps which can mimic the behaviour of a passive one-sided grounded coil (inductor).
    The core of this circuit is the so-called "generalized impedance converter (GIC)" which often is used as a replacement for an inductor in active filters and oscillator circuuits.
    This GIC based active inductor consists of two equal opamps, 4 equal resistors and one capacitor and the "simulated" inductance is L=R²C (unit is Henry).
    It has been prooved that this circuit can replace a grounded inductor in the time as well as in the frequency domain.
    And the "inductive" behaviour of the circuit can be verified using the voltage storage capabilities of the capacitor.

    PS: Keyword GIC can be found in wikipedia.
  12. Sep 2, 2015 #11

    jim hardy

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    that's a handy circuit

    i once used this one, from old National appnote AN31 ?



    but GIC is new to me.....

    if every day i learn something new, i should eventually know something.

    old jim
  13. Sep 3, 2015 #12


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    Doesn't seem to be one. Do you have a link you like for GIC. Can it emulate ideal inductors? or is it someone limited like the Gyrator.
  14. Sep 3, 2015 #13


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    I would love to change all instances of the word "resists" to "opposes" in my post #4 as suggested by William White in post #5. He is absolutely correct.

    Yet another summary of that which precedes:

    A growing field cuts through coil turns inducing a current that opposes the growing current that is causing the field. And vice versa: A shrinking field cuts through the coil turns and induces a current that opposes the reduction in current that is shrinking the field. The inductor naturally opposes any change in current. This causes it to impede AC currents (quantified as impedance).

    Inductor Field energy increases or decreases with the square of the current. ½ L I2
    The current change either requires that energy be supplied to the field (for increasing current) or be dissipated externally (for decreasing current).

    When the current is shut off abruptly and completely, the ideal inductor will create an infinite voltage to maintain the current flow and dissipate its stored energy. Sparks will generally ensue.
  15. Sep 3, 2015 #14


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    Sorry - you are right. I was of the opinion that wiki has a description. As it seems - that is not the case.
    Here is a good link (GIC for an "ideal" inductor - as far as a real opamp does allow it):

    (Sorry - this works only if you are registered/logged in to the site). Therefore, I have nclosed a pdf paper (active inductor on page 10).

    Such a two-opamp circuit is often used in active filters (active realization of LRC structures).

    A comment to Jim Hardy`s circuit: This is one version of a LOSSY inductor; however, I think it is an equivalent to a real inductor (coil) in the frequency domain only (sinusoidal signals in the time domain).
    It does not mimic the true step response of a lossy inductor.

    Attached Files:

    Last edited: Sep 3, 2015
  16. Sep 19, 2015 #15
    Hey Curious,

    Basically, time varying magnetic flux through the inductor is generated by the time varying current (magnetic fields are generated by currents through wires and moving charges) flowing through the inductor (remember inductors only have an effect for time varying currents). We know from Faraday's law and Lenz's law that a voltage is induced across the inductor in such a way that it produces a current that opposes the change in the flux caused by the original changing current. Generally, Faraday's law and Lenz's law are axiomatic descriptions of nature but really there are more fundamental explanations for these phenomena based on special relativity. Basically, nature does not like changing magnetic flux/fields and generates EMFs (voltages) that resist these changing fluxes (and in turn resists the change in the current). Also, I think Jim's analogy to inertia for massive bodies is excellent and I never thought about it quite that way before.

  17. Sep 30, 2015 #16
    Hi All,

    Silly question here i'm sure. But.

    Why does current not travel the shortest distance across an inductive coil (if the coils are physically touching and not insulated) instead of all the way through the coil.

    Any insight.

  18. Sep 30, 2015 #17


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    In that case, you'd expect it would take the shortest/easiest path, and it will; the consequence being that it won't show the value of L you'd designed for. So because we need the current to follow the full path along the wire you must space the turns so each is separated from its neighbours by an air gap, or else coat the wire with another form of insulation.
  19. Sep 30, 2015 #18
    Thanks for the reply NascentOxygen,

    So If the windings are touching in an Inductor, transformer, motor/generator etc they will always have a form of insulation?
    What has thrown me is that in some pictures of the components stated it looks like there is no insulation, but from your reply I assume that there would be some sort of clear insulating varnish or something similar.


  20. Sep 30, 2015 #19
  21. Sep 30, 2015 #20


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    As NO says, they are generally insulated. "Magnet Wire" has very thin insulation, since the voltage between adjacent turns is usually low. You can get magnet wire with standard thin insulation, or with "double build" or "triple build" insulation thicknesses, if you need more insulation or if you need the extra physical strength (with very fine magnet wire).
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