A capacitor looks like a part that just stores charge. Watch it the right way and it's something else entirely: a device that responds to change, never to state. It ignores what's holding still and passes only what moves — which is the most basic act of communication there is.
Every claim in this series unspools from i = C·dv/dt. In words: the current flowing "through" a capacitor is proportional to how fast the voltage across it is changing — its rate, its slope — and not at all to the voltage itself.
Sit a steady voltage on it and nothing flows: a flat line has zero slope, so i = 0. The capacitor is, to a constant, invisible. But move that voltage — ramp it, wiggle it, edge it — and current flows in exact proportion to the steepness of the move. Steeper change, more current. Reverse the change, reverse the current.
A capacitor cannot see a message that holds still. It only ever reports the difference.
That single fact is why a capacitor is a communicator and not just a bucket. A bucket tells you how full it is. A capacitor tells you the moment the level changed — and change, not level, is where information lives.
Before change can mean anything, see the resting state. Two plates, a voltage across them, charge piling up on the faces, a field strung between. Drag the voltage and watch charge follow: Q = C·V. This is the still picture — the thing the next instrument will set in motion.
Note what this still picture can't tell you: nothing here is a message yet. A held charge is a held state. To communicate, the slab has to move — and the instant it does, the next instrument lights up.
Here is the whole thesis as a moving instrument. The amber trace is the voltage you drive onto the plate. The cyan trace is the current that flows in response — and it is, exactly, the slope of the amber. Drive a flat stretch (a held level, a DC bias) and the cyan flatlines to zero: the capacitor blocks DC by ignoring it. Drive an edge and the cyan spikes. Drive a fast wiggle and the cyan dances harder than the amber.
Flat voltage → zero current. The capacitor is deaf to anything that isn't moving — and that deafness is the DC block, the first real comms trick in the kit.
i = C·dv/dt, no resistance, no leakage, no dielectric loss. Real parts add series resistance (ESR), finite leakage, and frequency limits, which is exactly what the later instruments (the RC filter, the coupling cap) will bring in. The ideal is the right place to start because the comms behavior — change-not-state — is already complete here; the real-world terms only shape it.
Try the pure DC setting: a steady voltage, and the current trace is a dead flat line on zero. Then sine: the current is a sine too, but shifted a quarter-turn — peaking where the voltage is changing fastest (at the zero-crossings), zero where the voltage is momentarily still (at the peaks). That quarter-turn shift is the signature of a derivative, drawn live. The capacitor isn't lagging — it's reporting the rate.
Everything else capacitors do in communication is this one behavior, dressed for a job. Block the DC and pass the signal — that's a coupling capacitor. Pass some rates of change and not others — that's a filter. Let the change leap a gap with no wire — that's capacitive coupling, and it's the same displacement current Maxwell needed to finish his equations. The foundation you just watched is the whole channel in seed form.
Stack the rest when you're ready — each one is this same equation, pointed at a new job.