Reactance

8 Articles

When Electricity Doesn’t Take The Shortest Path

January 13, 2026 by 48 Comments

Everyone knows that the path of least resistance is the path that will always be taken, be it by water, electricity or the feet of humans. This is where the PCB presented by [ElectrArc240] on YouTube is rather confusing, as it demonstrates two similarly sized traces, one of which is much shorter than the other, yet the current opts to travel via the much longer trace. If you were to measure this PCB between each path, the shorter path has the lowest resistance at 0.44 Ω while the longer path is 1.44 Ω. Did the laws of physics break down here?

Of course, this is just a trick question, as the effective resistance for an electrical circuit isn’t just about ohmic resistance. Instead the relevant phrasing here is ‘path of least impedance‘, which is excellently demonstrated here using this PCB. Note that its return path sneaks on the back side along the same path as the long path on the front. To this is added a 1 MHz high current source that demonstrates the impact of alternating current, with reactance combining with the resistance.

Although for direct current it’s fair to say that impedance is the equivalent of resistance, once the inductance of a trace has to be taken into account – as in the case of AC and high-frequency signaling – the much higher inductance of the short path means that now the long path is actually the shortest.

When you are doing some impedance matching in your favorite EDA software while implementing an Ethernet RMII link or similar, this is basically part of the process, with higher frequencies requiring ever more stringent mechanisms to keep both sides happy. At some point any stray signals from nearby traces and components become a factor, never mind the properties of the PCB material.

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Deriving The Reactance Formulas

April 28, 2025 by 9 Comments

If you’ve dealt with reactance, you surely know the two equations for computing inductive and capacitive reactance. But unless you’ve really dug into it, you may only know the formula the way a school kid knows how to find the area of a circle. You have to have a bit of higher math to figure out why the equation is what it is. [Old Hack EE] wanted to figure out why the formulas are what they are, so he dug in and shared what he learned in a video you can see below.

The key to understanding this is simple. The reactance describes the voltage over the current through the element, just like resistance. The difference is that a resistance is just a single number. A reactance is a curve that gives you a different value at different frequencies. That’s because current and voltage are out of phase through a reactance, so it isn’t as easy as just dividing.

If you know calculus, the video will make a lot of sense. If you don’t know calculus, you might have a few moments of panic, but you can make it. If you think of frequency in Hertz as cycles per second, all the 2π you find in these equations convert Hz to “radian frequency” since one cycle per second is really 360 degrees of the sine wave in one second. There are 2π radians in a circle, so it makes sense.

We love developing intuition about things that seem fundamental but have a lot of depth to them that we usually ignore. If you need a refresher or a jump start on calculus, it isn’t as hard as you probably think. Engineers usually use vectors or imaginary numbers to deal with reactance, and we’ve talked about that too, if you want to learn more.