# How does the magnetic field of an inductor affect the operation of a DC circuit?

I was reading about the operation of inductors in DC circuits on the website All About Circuits, and I'm a bit confused on how an inductor operates in a DC circuit.

So far, I understood that any current flowing through a conductor will produce a magnetic field force and, consequently, a magnetic field flux, which is perpendicular to the conductor. And by making the conductor coil-shaped, the magnetic field flux will increase because it gets concentrated.

So far this is kinda clear.

But then two sentences confused me:

1. Whereas an electric field flux between two conductors allows for an accumulation of free electron charge within those conductors, a magnetic field flux allows for a certain “inertia” to accumulate in the flow of electrons through the conductor producing the field.

What do they mean by inertia accumulating in the flow of electrons?

What I understood from this sentence is that eventually the magnetic field force will become so high that it will prevent any more current from flowing. However, I know that magnetic field flux is perpendicular to the conductor, so I don't see how it can prevent the current from flowing. This is why I'm confused and why I think they mean something else by inertia.

2. As the electric current produces a concentrated magnetic field around the coil, this field flux equates to a storage of energy representing the kinetic motion of the electrons through the coil.

From this sentence I understood that magnetic field flux is the equivalent of energy in the inductor. And of course this energy was taken from the circuit's voltage source, so if this energy becomes equal to the energy supplied by the voltage source, shouldn't it, eventually, prevent any more current from flowing through the circuit?

I'm really confused in here...

• It's good that you quote the text in question but you should also give a link to the original source so one can get the context if needed. – Curd Mar 16 '18 at 10:58

Unfortunately, your source does not have a good understanding of physics, so has chosen some bad analogies. 'Inertia of electron flow' is harking back to the water flowing through pipes analogy, which is OK for voltage, current and resistors, but gets stretched too far when it comes to inductors.

Current flowing in the wires of an inductor create a magnetic field in the inductor core, which is at right angles to the wire.

Energy is stored in the magnetic core of the inductor. This energy has come from the power supply's energy source. Energy is stored as the magnetic field, and has nothing to do with kinetic energy. It's stored in the field, just as an electric field stores energy between two conductors at different voltages. What the field is is best left to quantum physics. You can think of a field as stretchy rubber sheet if you like. It isn't, but it helps some people.

It's this stored energy that drives the 'unusual' behaviour of capacitors and inductors. Capacitors store energy as the square of the voltage. Inductors store energy as the square of the current. If you try to change their voltage or current (respectively), you have to change the stored energy. If you try to do this quickly, then it requires (or generates) a high power (energy change per time). If you've ever short-circuited a big capacitor, or open-circuited a big inductor, you'll know what a spark you get.

There are two limits to how much current can usefully be pushed into an inductor, but neither has to do with the magnetic field interacting with the wires.

The first is heat. The current generates heat in the resistance of the wire, and the first thing to fail as the temperature rises is usually the wire insulation. So as long as it's limited to a very short time, very large currents can be applied, before the temperature rises too far.

The second is magnetic saturation. At a certain current, the core reaches its maximum field, and its permeability drops. Higher current (up to the thermal limit) will not damage the inductor, but its inductance value will have dropped radically, and little more energy can be stored. It's the practical limit for operation. If the inductance value is being relied on to limit a changing current, onset of saturation is a bad thing and usually results in a further sudden increase of current.

A useful mental model of a inductor for the purpose of designing circuits is that inductors impart inertia to current. This is false and non-sensical at the physics level, but a useful abstraction when trying to picture what a inductor does in a circuit.

Consider current running thru a piece of wire. There is always some unavoidable inductance, but for individual wires it's usually so small we can ignore it. Let's say you connected this wire to a 5 V source with 5 Ω in series across the ends of the wire. As soon as you connect it, 1 A will flow instantly. When you disconnect it, the current stops flowing instantly and goes to 0 A.

Now replace that wire with a inductor. When you first connect it, the current will ramp up, not jump to the final value instantly. Actually, the current is a exponential that asymptotically approaches the steady state value of 1 A. The larger the inductor, the larger the time constant.

One way to mentally picture this (again, don't try to think of the physics this way) is that the inductor gives inertia to the current. When you first connect the "push" (the voltage), the current starts going up.

Now think of what happens when the circuit is opened. The current thru the inductor doesn't want to stop suddenly, just like a car going down the road can't stop suddenly. It takes a sustained force over some time to stop the car.

Likewise, it takes a sustained reverse voltage over some time to stop the current. But I can hear you thinking, we just opened the circuit, so there can't be any current. The problem is that this is a case where the approximation of all components being ideal breaks down. Somewhere there is a switch that has to open to stop the current flowing. That could be a transistor or a mechanical contact.

Let's look at what happens as a mechanical contact opens. It can't instantly jump from connected to far apart. At some point, it just starts to open, and there is a very small air gap between the contacts. Due to the "inertia" of the current, the current can't change instantaneously. Immediately after the contacts open, the voltage goes high enough to arc across the little air gap, which continues to allow current to flow. That does cause some voltage across the switch, which applies reverse voltage across the inductor, which cause the current to decrease. Eventually the current goes to 0, and everything is back to the open-circuit steady state.

You may have a problem imagining how this inductor can make a high voltage. Think of the car being slowed down. When it is slowed down normally, the brakes cause a reverse force, which causes the speed to go down until it eventually gets to 0. However, trying to open the circuit quickly with a mechanical switch is like the car hitting a solid wall. The reverse force gets very high. Due to being so high, it stops the car quickly (and in this case destructively).

In the case of a inductor and mechanical switch opening, it's the switch that gives a bit, unlike the car hitting a wall where the car gives instead of the wall.

Go back to the basic equation of what a inductor does, and you can see this behavior described mathematically:

dI = V dt / L

A voltage (V) applied for some time (dt) cause a current increment (dI) inversely proportional to the inductance (L). In common units:

dA = V ds / H

dA is the current increase in Amperes, V the voltage, ds the seconds the voltage is applied, and H the inductance in Henries.

For example, if you apply 5 V to 100 mH for 30 ms, the current rise in the inductor will be (5 V)(30 ms)/(100 mH) = 1.5 A.

This ability of a inductor to make a high voltage when you try to stop the current thru it quickly is the basis for how boost converters work. First, the inductor is "charged up" by connecting it between the input supply and ground. This is done by closing the switch. That causes the current thru it to rise linearly.

When the current gets to a nice level, the switch is opened. The inductor current can't stop instantaneously. The inductor makes whatever voltage it takes to keep the current flowing in the short term. The current therefore flows thru the diode, charging the output capacitor. This puts reverse voltage across the inductor, reducing its current over time.

This switch is then closed again. That stops current from flowing to the output, but builds up current in the inductor. This process repeats rapidly to deliver lots of little shots of current to the output.

• I like your car flyback force multiplier, +1. – Neil_UK Mar 16 '18 at 11:16
• I can't fully grasp the meaning of the sentence: "the inductor gives inertia to the current" Is it the same as saying it prevents the current from suddenly stopping? – DigiNin Gravy Mar 16 '18 at 13:40
• current has no inertia but the magnetic field has, or even better: the magnetic vector potential carries momentum, hence the "inertia". – hyportnex Mar 23 '18 at 13:12

You asked how an inductor affects the operation of a DC circuit. Strictly speaking, a DC circuit has a constant current, which means that an ideal inductor behaves exactly like a short-circuit. There is a zero voltage drop across it and it neither helps nor hinders the flow of the constant current.

The only time the inductor has any effect is when there is a change in current, like when you open or close a switch in the circuit. When that happens, the inductor resists any change in current; it tries to keep the current the same as before. This is the "inertia" that the "All About Circuits" website describes.

The magnetic flux is like a heavy flywheel that tends to keep the current flowing at the same rate. To change the current, you have to apply a force to the flywheel to speed it up or slow it down. The bigger and heavier the flywheel, the bigger the inductance, and the harder it is to change the current.

The following website (which I wrote) might help you understand the concept better:

http://ataridogdaze.com/science/hydraulic/index.html

Click the "Inductor" link to watch the video or read about the analogy between an inductor and a flywheel.