#### VooDust

Joined Oct 21, 2019
4

At the beginning of the current through the inductor, the opposition to the current (positive voltage) is at it's peak - I get that. But if there is opposition, then not as much current would flow, invalidating the assumption about the amount of changing current in the beginning? I mean how can changing current induce opposition that would prevent the current from changing in the first place?

Another thing that is confusing is that when reading about inductors, they always talk about that 90° phase shift between current and voltage. But that 90° shift pertains only to the voltage/current across the inductor, induced by the inductor, not the whole circuit at hand, right? After all, I can't just take a circuit's wire, wind it around my screwdriver a couple times and suddenly the current curve of the whole circuit lags the voltage curve by 90°?

Intuitively, and with the help of circuitlab.com, I come to the conclusion that inserting a very small inductor into the circuit would not be noticeable at first. Gradually increasing the inductor in size will slowly create a lagging current curve in the circuit, while also gradually attenuating the signal, i.e. less current overall / smaller current amplitude. By the time that the inductor is so large to induce a current lag of 90° in the whole circuit, it would be so large that practically no current would flow?

Every resource I consult keeps repeating the same paradigms over and over like "the inductor wants to keep current flowing" but that does not really help me much. I wonder if I just don't get it. How would I go about plotting a circuit's voltage and current curve, knowing that the voltage that can be dropped by the inductor at di/dt times henrys equals such and such volts?

Last edited:

#### Papabravo

Joined Feb 24, 2006
19,617
The dynamics of the relationship between current and voltage and current are governed by a 1st order differential equation. If you don't know what that is then the heuristic (hand waving) explanations are likely to create the confusion which is manifestly obvious. If you were to make the effort to learn just enough calculus to understand that differential equation, the clouds might lift. In case you have some calculus, the equation is:

$$V_{L}\;=\;L\frac{dI_{L}}{dt}$$

#### ericgibbs

Joined Jan 29, 2010
16,842
hi VD,
If you do not know the maths, these simple simulations will show the idea.
One shows the Freq/Phase response [phase dotted line] the other the Sinewave format, note the 'Shift' is also in the resistive load.

E

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#### VooDust

Joined Oct 21, 2019
4
Unfortunately I flunked calculus at school. I always found the things you could do with it fascinating though. I think I must give it another try and learn some of it in my spare time.

Thanks for the pictures, much appreciated. I think the general idea is clear. For the detailed questions in my first post I guess it's not much use trying to explain without the aid of calculus.

#### BobTPH

Joined Jun 5, 2013
6,101
I mean how can changing current induce opposition that would prevent the current from changing in the first place?
An ideal inductor has no resistance and thus, if you applied any voltage across it, infinite current would suddenly start flowing. But the changing current creates a changing magnetic field, and that changing magnetic field creates a voltage that opposes the current. How much does it oppose the current? We can only determine this by using calculus. Calculus allows us to examine what happens during very small time intervals, and then see what happens as we make these intervals smaller and smaller. If we are lucky (and we are with all physical systems), the behavior converges to a limit when the intervals become infinitesimally small. And this gives us the real behavior. The result is the equation posted by @Papabravo. In an ideal inductor, with a forced voltage across it, the current will start at zero and then increase linearly forever. Fortunately, there are no ideal inductors. So what happens is the current is eventually limted by the resistance in the circuit.
Another thing that is confusing is that when reading about inductors, they always talk about that 90° phase shift between current and voltage. But that 90° shift pertains only to the voltage/current across the inductor, induced by the inductor, not the whole circuit at hand, right?
Right, the analysis of an inductor you are reading applies only to the voltage across and the current through and ideal inductor. How could it be otherwise, since the rest of the circuit that the inductor is part of could be anything? If there is resistance in the circuit, for example, the voltage and current in the resistor will still be perfectly in phase as they always are. If the inductor itself has resistance (which real inductors all do) then the phase will never be exactly 90 degrees, it will be a combination of the phase of the inductive current and the resistance current. Actually there is also capacitance, which has a phase shift in the opposite direction. So it take a complex number to describe the full relationship of current to voltage with all three components (resistive, inductive and capacitive) simply adding as complex numbers.

Bob

#### Jony130

Joined Feb 17, 2009
5,435

#### WBahn

Joined Mar 31, 2012
27,946

View attachment 189328

At the beginning of the current through the inductor, the opposition to the current (positive voltage) is at it's peak - I get that. But if there is opposition, then not as much current would flow, invalidating the assumption about the amount of changing current in the beginning? I mean how can changing current induce opposition that would prevent the current from changing in the first place?

Another thing that is confusing is that when reading about inductors, they always talk about that 90° phase shift between current and voltage. But that 90° shift pertains only to the voltage/current across the inductor, induced by the inductor, not the whole circuit at hand, right? After all, I can't just take a circuit's wire, wind it around my screwdriver a couple times and suddenly the current curve of the whole circuit lags the voltage curve by 90°?

Intuitively, and with the help of circuitlab.com, I come to the conclusion that inserting a very small inductor into the circuit would not be noticeable at first. Gradually increasing the inductor in size will slowly create a lagging current curve in the circuit, while also gradually attenuating the signal, i.e. less current overall / smaller current amplitude. By the time that the inductor is so large to induce a current lag of 90° in the whole circuit, it would be so large that practically no current would flow?

Every resource I consult keeps repeating the same paradigms over and over like "the inductor wants to keep current flowing" but that does not really help me much. I wonder if I just don't get it. How would I go about plotting a circuit's voltage and current curve, knowing that the voltage that can be dropped by the inductor at di/dt times henrys equals such and such volts?
Saying "at the beginning of the current" is a bit ambiguous and might be leading you astray. If you have a sinusoidal voltage across and current through an inductor, the when the current is passing through zero, the rate at which the current is changing is at its peak and this is why the voltage across the inductor is at its peak. At the moment of peak current is when the rate of change of current is zero and this is why the voltage across the inductor is zero at this moment.

The reason that inductors resist changes in the current has to do with the interactions between changing magnetic fields and changing electric fields, as governed by Maxwell's Equations. Magnetic fields are generated by electrical currents and so if the current is changing, the magnetic field is changing. But a changing magnetic field induces an electric field that attempts to make current flow in an conductor and the physics works out (and is known as Lenz's Law) that it does so in the polarity that opposes that change in the current that is causing the change in the magnetic field. You can think of it something like inertia -- you have to apply a force (voltage) not to make things move, but to change the existing motion. Just like Newton's First Law -- if I have an object either at rest or in motion, it will continue doing that unless I apply a force to it which causes a change in the velocity. The same things with an inductor and current. If I have a current (be it zero or some non-zero value), it will want to continue doing that unless I apply a voltage across the inductor which then causes a change in the current.

You are correct that just putting a bit of inductance into a circuit does not change the overall current/voltage relationship. The 90° phase relationship applies ONLY to the voltage across the inductor and the current through the inductor. So if you insert a tiny inductance into an AC circuit, there will be a tiny voltage drop across the inductor and that tiny voltage will be 90° out of phase with the current flowing through the inductor, but that tiny voltage will have very little impact on the voltages elsewhere in the circuit. As you increase the inductance, the impact of the inductor's voltage becomes more pronounced and, at some point (depending on the specifics of the circuit) it becomes the dominant factor in the overall circuit's V/I relationship.

Without getting into the calculus, you can plot the voltage and current across a conductor pretty easily using a spreadsheet.

The key relationship that we can exploit is that di/dt ~= delta i / delta t.

Make a column that gives time in equal increments over a couple of periods of your waveform. Then put a column that gives the current at that time. For the next column calculate the change between the current at the present time and the current in the row just above it. Now compute the voltage by using multiplying the inductance by the ratio of the change in current to the change in time between the present row and the prior row.

#### WBahn

Joined Mar 31, 2012
27,946
An ideal inductor has no resistance and thus, if you applied any voltage across it, infinite current would suddenly start flowing.
No, it would ramp linearly and continue increasing without bound (as you describe later on).

Fortunately, there are no ideal inductors. So what happens is the current is eventually limted by the resistance in the circuit.
Superconducting magnets are pretty good ideal inductors. The current isn't limited by the resistance in the circuit, but instead either by the ability of the power supply to continue providing the ever increasing current needs or by the critical parameters of the superconductor being reached and thus driving it out of the superconducting state.

#### MrChips

Joined Oct 2, 2009
27,738
Another way of understanding circuits with inductors (and also capacitors) in AC applications is to use complex numbers.

The impedance of a resistor R is R ohms.
The impedance of an inductor L is jwL ohms.
The impedance of a capacitor C is 1/(jwC) ohms.

When you begin to combine L and C in a circuit you will be able to unravel the current, voltage, and phase angle using complex arithmetic.

#### BobaMosfet

Joined Jul 1, 2009
2,053

View attachment 189328

At the beginning of the current through the inductor, the opposition to the current (positive voltage) is at it's peak - I get that. But if there is opposition, then not as much current would flow, invalidating the assumption about the amount of changing current in the beginning? I mean how can changing current induce opposition that would prevent the current from changing in the first place?

Another thing that is confusing is that when reading about inductors, they always talk about that 90° phase shift between current and voltage. But that 90° shift pertains only to the voltage/current across the inductor, induced by the inductor, not the whole circuit at hand, right? After all, I can't just take a circuit's wire, wind it around my screwdriver a couple times and suddenly the current curve of the whole circuit lags the voltage curve by 90°?

Intuitively, and with the help of circuitlab.com, I come to the conclusion that inserting a very small inductor into the circuit would not be noticeable at first. Gradually increasing the inductor in size will slowly create a lagging current curve in the circuit, while also gradually attenuating the signal, i.e. less current overall / smaller current amplitude. By the time that the inductor is so large to induce a current lag of 90° in the whole circuit, it would be so large that practically no current would flow?

Every resource I consult keeps repeating the same paradigms over and over like "the inductor wants to keep current flowing" but that does not really help me much. I wonder if I just don't get it. How would I go about plotting a circuit's voltage and current curve, knowing that the voltage that can be dropped by the inductor at di/dt times henrys equals such and such volts?
You have valid questions- the problem is how you're being taught. Stop reading that chapter, and go read about how an inductor behaves in a DC environment. Which is represented by the 1st quarter of your graph in the above picture. Once you have that, the rest will make sense.

I recommend this book-

Title: Understanding Basic Electronics, 1st Ed.
Publisher: The American Radio Relay League
ISBN: 0-87259-398-3

Meanwhile, view this:

#### crutschow

Joined Mar 14, 2008
31,156
I mean how can changing current induce opposition that would prevent the current from changing in the first place?
The inductor has an impedance that resists a change in current, similar to the way the interitia of an object resists any change it its velocity.
Similarly the current in an inductor tends to stay flowing due to the inductance, much the same as the inertia of an object tends to maintain its velocity (both would continue indefinitely if all resistance/friction/losses are eliminated)..
But that 90° shift pertains only to the voltage/current across the inductor, induced by the inductor, not the whole circuit at hand, right?
Yes, the 90° phase-shift pertains only the relation between the current through (not across) the inductor versus the voltage across the inductor.

#### MrAl

Joined Jun 17, 2014
9,640

View attachment 189328

At the beginning of the current through the inductor, the opposition to the current (positive voltage) is at it's peak - I get that. But if there is opposition, then not as much current would flow, invalidating the assumption about the amount of changing current in the beginning? I mean how can changing current induce opposition that would prevent the current from changing in the first place?
Hi,

As to your last sentence, the changing current does not 'prevent' the current from changing, It prevents the current from changing TOO FAST. There's a big difference.
For example, connect a 1 ohm resistor in series with an inductor and all in series with a 2 volt battery. When you connect the circuit at first no current or very little current flows, but then as time progresses, eventually the current goes up to 2 amps. That 2 amps is only because of the resistor the inductor now looks like a short circuit. That's because the time it had to limit the change in current had passed and now we see the maximum current flow. And during that time, the rate that the current could change was limited because the current was producing a stronger and stronger magnetic field and moving electrons interact with magnetic fields and changing magnetic fields interact with electrons. Thus there is interaction between the two.
This interaction does not cause a road block it's more like a valve that limits the flow.
The main point though is that magnetic fields interact with electrons when one or the other or both are changing (position or field strength and direction).

#### RBR1317

Joined Nov 13, 2010
706
I think I must give it another try and learn some of it in my spare time.
What many people may not realize is that real engineers don't use calculus for circuit analysis, they use Laplace transforms (and tables of inverse Laplace transforms) to formulate circuit equations for RLC networks in the complex frequency domain as though it were just resistors with DC sources. Of course, one is limited by the extent and thoroughness of the transform tables available. And to understand why the Laplace transform method works does require a deep understanding of the calculus. Just suggesting that learning to use Laplace transform tables for circuit analysis might be a productive use of one's spare time.

#### MrAl

Joined Jun 17, 2014
9,640
What many people may not realize is that real engineers don't use calculus for circuit analysis, they use Laplace transforms (and tables of inverse Laplace transforms) to formulate circuit equations for RLC networks in the complex frequency domain as though it were just resistors with DC sources. Of course, one is limited by the extent and thoroughness of the transform tables available. And to understand why the Laplace transform method works does require a deep understanding of the calculus. Just suggesting that learning to use Laplace transform tables for circuit analysis might be a productive use of one's spare time.
Hi there,

I use Laplace Transforms for almost everything but i also use ODE's because they lend themselves really well to numerical solution on even the regular home computer. There are various methods to do this and are not that hard to program if you are into writing your own programs. A method could be as simple as:
v=v+h*dv/dt

where dv/dt is the derivative (ODE) found from the circuit and 'h' the step size.

#### SamR

Joined Mar 19, 2019
4,496

#### SamR

Joined Mar 19, 2019
4,496
This seems to be the 11th edition:
Amazing... Dunno how they can do that with a book currently in publication that lists for ~\$110!?!? Good 'un Bertus! Would save a lot of money to spend on beer for a student...

#### VooDust

Joined Oct 21, 2019
4
Hi all, thank you so much for your inputs, it's more that I can chew right now, but I'll go at it step by step. I think I'll start with a proper book like you mentioned.

Enough of the hand waving youtube tutorials.

#### JMW

Joined Nov 21, 2011
137
Unfortunately I flunked calculus at school. I always found the things you could do with it fascinating though. I think I must give it another try and learn some of it in my spare time.

Thanks for the pictures, much appreciated. I think the general idea is clear. For the detailed questions in my first post I guess it's not much use trying to explain without the aid of calculus.
I know what you mean by calc. When I get ambitious, I go to Kahn academy, they have tutorials that really conquer my insomnia

#### KeepItSimpleStupid

Joined Mar 4, 2014
5,088
You missed the following simple rules:

The current in an inductor cannot change instanstaneousy.
The voltage across a capacitor cannot change instataneously.

The other concept is that inductors and capacitors are not ideal. They have parasitics. A real inductor has a resistance. This resistance initially limits the current.