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, the 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 is the flow of electric charges through a point in the circuit. Its unit — the ampere (A) — is defined as the travel of travel about 6.24 × 1018 elementary charges per second via a particular spot. That exact number, known as one coulomb, isn’t worth memorizing, but it neatly relates the ampere to other SI units of measure.
The “elementary charge” in this definition is typically the electron, but 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 aren’t contained within the wire (although they usually hug the shape).
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. 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 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 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. It is always a delta between two points; if one of the endpoints is not specified, the reference is usually the negative supply rail.
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 squeeze onto its plates when 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.
Capacitive elements impede the flow of currents in a frequency-dependent way. The magnitude of this effect — known as capacitive reactance — is described by the following formula:
(A negative sign is sometimes thrown in to distinguish it from inductive reactance.)
Like resistance, capacitive reactance is measured in ohms, and has a superficially similar effect on currents and voltages. That said, it is a distinct physical phenomenon. One of the more important distinctions is that in a resistor, the current through the device is in lockstep with the applied voltage. In a capacitor, the voltage across the terminals rises only some time after the current starts flowing; for repetitive sine waves, the lag is 1/4th of a cycle. This property can be helpful when designing oscillators, but it is the bane of op-amp feedback loops.
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 delta of 1 A per second, momentarily opposes this (rather leisurely!) change by developing 1 volt across its terminals.
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 down the line.
“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. Although there is a mathematical model od impedance that involves complex numbers, most of the time, the term is simply a stand-in for 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.
For a catalog of other articles on electronics, click here.