Understanding Inductors: Principles, Working, and Applications

Inductors aren’t as famous as their passive counterparts, the resistor and capacitor, and, strangely, it can sometimes seem like you spend more time dealing with unintentional inductors than the actual parts. But they are still a critical, even foundational, part of the circuits and electronics. In this tutorial, we’ll learn about inductors, how to treat them in both AC and DC circuits, as well as discussing why they work the way they do and what applications you can find them in.

An inductor, physically, is simply a coil of wire and is an energy storage device that stores that energy in the electric fields created by current that flows through those coiled wires. But this coil of wire can be packaged in a myriad of ways so that an inductor can look like practically anything. Fortunately, for a schematic, the variations are more limited, and all representations of inductors are some variant of something that looks like looping wires.

The ability to store energy in the electric fields is measured in the units of henry, or henries, named after the guy who discovered the principle of inductance. For most real-life scenarios, particularly for electronics applications, most inductors are a small fraction of a henry. Now that we’ve briefly gone over what inductors are and what they look like, let’s see how they act in circuits and why they can be important.

In DC circuits, inductors are very simple to work with. You can just replace any inductor in a steady-state DC circuit with a short circuit. If you remember that an inductor is, fundamentally, a coil of wire, this should seem rather unsurprising. If an inductor is in parallel with other components, you can disregard those components, as it will be like you short-circuited their nodes together.

In transient DC circuits, or circuits where you’re measuring what happens in a short period of time after a change, inductors are a little more complicated. Inductors resist changes in current, so if there is a switch that closes and the voltage across an inductor changes from 0V, the voltage will try to change instantaneously but the current through it will take some time to ramp up to its steady state current. As current is a result of a voltage, this causes some strange effects on the voltage. Let’s look at the equation that describes the voltage across an inductor in relationship to the current through the inductor.

As you can see, voltage is equal to the inductance (in henrys) multiplied by the rate of change through the inductor (in amps per second). Looking at a steady state DC signal, where current is flowing through an inductor consistently, you won’t see a voltage across the inductor. But if you flip a switch and there’s a voltage trying to drive a current through the inductor, the inductor will “fight” the change in current by generating its own voltage. The most common way we see this in action is with a vacuum cleaner.

Vacuum cleaners are just a collection of motors and motors are just windings of wire that interact with magnets. So, motors are, from a certain point of view, simply inductors that also happen to move. Thus we can say that a vacuum is a very inductive load and will share many characteristics. If the switch is on with a vacuum cleaner and you either plug it in or unplug it, it's very common to see a spark generated at the outlet. Let’s take the case of unplugging the vacuum cleaner. This inductive load has about 120V across the load and is storing energy in its magnetic field while drawing about 10 amps of current. If we unplug the vacuum without using the switch, the energy in the magnetic field is used to resist the instantaneous change in current. It does so by generating a very large voltage - large enough to cause a breakdown in air, pulling current across the air gap in the form of a spark.

So, for DC steady-state and transient circuits, you can either think of inductors as a short circuit or that they resist changes in current. With that summary, let’s look at how inductors work in AC circuits.

In an AC circuit, an inductor’s performance and behavior is dependent on different factors. The way they affect the circuit depends on two things.

1. The frequency of the signal in the circuit.
2. The inductance of the device.

Let’s look at the equation that is used to describe the impedance of an inductor in an AC circuit and use that to help our understanding of its behavior.

The ‘j’ shows how the impedance of an inductor is imaginary, which, the way it affects the real life behavior is by causing phase shifts between voltage and current in a circuit. This will be gone into more depth when we do our Circuits 201 series that focuses on AC circuits. We’ll touch on this just a little a moment, though. But let’s move on to the other portions at the moment.

The ω (omega) is the frequency of the signal in the circuit in radians per second. As always, remember that omega is 2pi*frequency - forgetting to change frequency to radians per second (and back) is a common mistake I have made and probably many others. The important thing to note here is that if the frequency is 0, then the overall impedance is zero. And if the frequency is nearly infinite, then the impedance will be nearly infinite. This makes sense with the idea that inductors don’t like changes in current.

Finally, the l (a lower case L) represents the inductance of the device in henries. Most inductors in electronic devices are significantly less than 1 henry. Again, we can see a linear relationship between impedance and inductance. The higher the inductance, the higher the impedance, the lower the inductance, the lower the impedance.

The only item about phase shifts that I want to address is that, since inductors resist changes in current, inductive circuits “lag”. What this means is that, as the voltage across the circuit changes, the corresponding current through the circuit is delayed a bit. So, if the voltage rises, it takes a bit for the current to increase. And this can be strange as, at inflection points, the voltage is moving in one direction (growing for example) while the current is still continuing in another direction (decreasing, in contrast with a growing voltage). We’ll get into the math that describes this shift later but it’ll help a lot if you understand conceptually what’s going on first.

As stated, an inductor is simply a coil of wires. So why would the shape of the wire cause such behavior? It is important to remember that electrons actually have mass and, as a large collection, this can cause more of an effect than one would expect. Indeed, if we ever are able to create tutorials on electromagnetic theory with extremely high frequency signals, a lot of time is spent just discussing how to deal with getting electrons to go where you want when they’re moving quickly. But, for inductors, you can just think about how electrons don’t corner well, and when they have to change directions frequently, they struggle with it. And, if they’re having to turn corners and change directions very quickly, they really struggle with it. That is simplified and I can visualize physicists spitting out their coffee while reading this, but for our purposes, that’s probably sufficient.

In an ideal inductor, we assume that it doesn’t have any resistance (ie, it acts as a short in DC circuits AND also doesn’t consume power) but in reality, there is a small resistance that means that inductors will consume power in both AC and DC circuits. They also have a touch of capacitance in them but this is almost always negligible.

The resistance of an inductor also limits the amount of current an inductor can conduct. In ideal circuits, you don’t even need to think about this but in a real life application, the inductor needs to be sized so that the current doesn’t overheat or melt the device.

Inductors are very important in circuits that deal with antennas or other high frequency circuits that need to have a good balance between capacitance and inductance. Also, as mentioned previously, inductors occur naturally in loads such as motors, electromagnetics, even things like speakers. So even if there isn’t an explicit inductor in a circuit, you can model many devices as if they were inductors.

Inductors are one of the most fundamental devices in circuits, a passive 2-terminal device that finishes the trifecta - resistor, capacitor, and inductor. They’re easy to deal with in ideal DC circuits but get more complicated as their impedance changes with frequency. And, as always, real life is always more challenging than the ideal situations we’re sometimes taught in class. With this foundation, you’re now ready to move onto more complicated, capable circuits!