# Primer: core concepts in electronic circuits

### Back to the basics: defining key concepts in electronics without breaking out a plumbing wrench.

I didn’t kick off this site with a specific set of topics in mind, but I always wanted it to offer more than just self-indulgent punditry — and for one reason or another, electronics emerged as an audience favorite. My circuit design articles don’t get as many clicks as the occasional opinion piece, but they’re evidently valuable to some readers — and all things considered, it’s not a bad way to put some meat on this Substack’s bones.

So far, I focused on what I see other hobbyists struggle with as they wean themselves off other people’s schematics or kits. But in doing so, I might have left out an important stepping stone: a brief discussion of key concepts used to describe what’s going on in a circuit in the first place.

Today, I’d like to close this gap with a couple of crisp definitions that stay clear of flawed hydraulic analogies, but also don’t get bogged down by differential equations or complex number algebra.

### Current (I)

Current is the flow of electric charges through a point in the circuit. Its unit — the ampere (A) — is defined as the travel of about 6.24 × 10^{18 }elementary charges per second through a particular spot. That exact number, known as one coulomb, isn’t worth memorizing; the value is chosen to neatly relate the ampere to other SI units of measure.

The “elementary charge” in this definition is typically the electron. It’s good to remember that the flow of current doesn’t involve electrons bumping into each other; instead, their drift is mediated at a distance through electromagnetic fields that extend into the surrounding space. The fields may be originating from other electrons in the same wire, but might as well be coming from somewhere else.

### Resistance (R)

Resistance is the opposition to the flow of steady current. Although this can happen in a couple of ways, the most prosaic mechanism is that all common materials impede the movement of electric charges to some extent through a mechanism that bears some conceptual resemblance to friction. The wasted energy excites the medium and is then dissipated as heat.

The unit of resistance is the ohm (Ω). It can be thought of as the resistance of a conductor that, when subjected to a current of one ampere, produces one watt of heat.

### Voltage (V)

Voltage is the measure of electromotive force between two points in a circuit. It can be thought of as a pressure difference in the electron gas. In most circumstances, it’s what would cause a current to flow if you dropped a metal wrench across the aforementioned two points.

The unit of voltage — the volt (V) — corresponds to the electromotive force needed to induce a current of one ampere through a resistance of one ohm. Voltage is always a delta between two points; if one of the measurement endpoints is not specified, the reference is usually the circuit’s negative supply rail.

There is a linear relationship between the voltage applied to a section of a circuit, its apparent resistance, and the current flowing through. In other words, if you know two of the values, you can trivially calculate the third:

### Capacitance (C)

Capacitance measures the ability of a component to store electric energy, most commonly in an internal electric field. A capacitor that allows a charge of one coulomb to accumulate on its plates when it’s subjected to one volt is said to have a capacitance of one farad (F). Another way to look at it is that a 1 F capacitor, when supplied with a constant 1 A current for one second, will be charged to 1 V.

Because charging and discharging takes time, capacitive elements impede the flow of currents in a frequency-dependent way. A capacitor placed in series with a signal blocks steady currents, but allows more to pass through as the frequency picks up. The magnitude of this effect — known as capacitive reactance* *— is described by the following formula:

The *2πf* part of the expression, sometimes shortened to *ω*, is the angular frequency. It translates hertz into radians per second - or, the distance traveled by a point on a circle with a radius of 1. Without getting too much into the weeds, it crops up here because the combined effects of reactance and resistance are commonly modeled in a two-dimensional polar coordinate system where one 360° turn corresponds to a single cycle of a sine wave.

Like resistance, capacitive reactance is measured in ohms, and has a superficially similar effect on alternating, sine-wave currents and voltages. That said, it is a distinct physical phenomenon that typically involves the storage of energy, rather than its loss.

Another important distinction is that in an ideal resistor, the current through the device is always in lockstep with the applied voltage. In a capacitor, in contrast, the voltage across the terminals starts rising only some time after the current starts flowing because of the time needed to charge the plates. For repetitive sine waves, peak voltage corresponds to zero current — an apparent lag of 1/4th of a cycle:

This phase difference is important when considering the cumulative effect of resistance and reactance in a circuit; although the units are identical, a naive sum will usually not do. We'll talk about the correct way to handle this in a followup article.

Beyond that, the shift can be helpful when designing certain types of oscillators, but is the bane of op-amp feedback loops.

### Inductance (L)

Inductance measures the ability for a component to resist the change in the current flowing through it. It’s normally associated with the storage of energy in magnetic fields, which soak up energy when the current is ramping up, and then keep pushing electrons for a while when any external electromotive force disappears.

The unit of inductance — one henry (H) — corresponds the behavior of a device that, when subjected to a current rising at a rate of 1 A per second, opposes this (rather leisurely!) change by developing 1 volt across its terminals. The effect is symmetrical, so if the current plunges, the voltage dips negative as the inductor is trying to sustain the flow.

Similarly to capacitors, inductors impede the flow of alternating signals in a frequency-specific way. A series capacitor blocks DC and attenuates low frequencies; a series inductor attenuates fast-changing signals while letting steady currents through.

For inductors, the magnitude of this effect is quantified by the following formula:

Once again, reactance is measured in ohms, but it’s not exactly the same as resistance. For one, similarly to to a capacitor, an inductor causes voltages and currents across the device to get out of phase — although in this instance, the voltage rises first, and the current catches up 1/4th of a cycle later.

### Impedance (Z)

“Impedance” is a common shorthand for the opposition to the flow of current that arises from the combination of resistance, capacitive reactance, and inductive reactance. Because the effects are not necessarily aligned in phase, the overall impedance is not a simple sum of all three; we’ll talk about this down the line. But never mind: most of the time, the term is used a stand-in for a scalar value representing the dominant of the three quantities.

Perhaps confusingly, the same term is also sometimes used to loosely categorize signal sources and loads. A low-impedance source is one that can deliver substantial currents. Conversely, a high-impedance one can deliver very little juice before the signal ends up getting distorted in some way. In the same vein, a low-impedance load is power-hungry, and high-impedance one is not.

The final abuse of the term is the concept of characteristic impedance, as discussed in the earlier article on signal reflections. It is relevant only when dealing with signal lines that are long in proportion to signal wavelength. For well-behaved conductors, this parameter has the following relation to the conductor’s measured inductance and capacitance:

Of course, one could include a host of other formulas and laws on this article. That said, they all build on the same common foundations — and with the right mental model in place, they should be relatively easy to grasp.

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*For a continuation, see this article. For a catalog of other articles on electronics, click here.*

edited Apr 30Its nice to see people still look at explaining the more intuitive approach. I was stuck with learning electronics for ages because of the water pressure analogy, and needing to break out the Maxwell equations. Ironically, many books published prior to 1980 follow

the intuitive approach for quite a lot of subjects, compared to now that has you memorize equations that you don't know what or how they came about. The only reason I progressed past is from reading Heaviside's lectures from the turn of the century.

The local charity that sells books can be a goldmine.

Minor nit that hung me up for a moment. I'm thinking you might have a surplus number of the word 'travel' in the description of current:

"[...] is defined as the travel of travel about 6.24 × 1018 elementary charges per second"