Why a Capacitor Blocks DC but Lets AC Through

“Capacitors block DC and pass AC” is one of those lines students repeat with total confidence and can’t actually defend. A capacitor is two conducting plates separated by an insulator — nothing in that construction looks like it should care whether the current trying to flow through it is steady or oscillating. It doesn’t, directly. What it cares about is something more specific: whether the voltage across it is still changing. Everything else follows from that one fact.

The current is a response to changing voltage, not a flow through anything

No charge ever crosses the gap between a capacitor’s plates — the insulator sees to that. What looks like “current through the capacitor” in a circuit is really current charging or discharging the plates: charge accumulates on one plate, an equal and opposite charge accumulates on the other, and the wire outside carries that charge to and from the plates even though nothing passes between them. The rate at which that charge builds up is exactly the current in the connecting wire, and it’s set by how fast the voltage across the capacitor is changing:

i = C (dV/dt)

This is the entire mechanism in one line. Current isn’t proportional to voltage here, the way it is for a resistor — it’s proportional to the rate of change of voltage. A capacitor doesn’t resist current the way a resistor does; it resists change in its own voltage, and current is just the bookkeeping of how much charge has to move to keep up with that change.

Steady DC makes dV/dt go to zero

Connect a capacitor to a DC source through a resistor and, at the instant the switch closes, the capacitor is uncharged and its voltage is genuinely changing — so current flows, exactly as i = C(dV/dt) demands. But that current is depositing charge on the plates, which raises the capacitor’s voltage, which narrows the gap between the capacitor’s voltage and the source’s fixed voltage, which lowers the current, which slows the rate of charging further still. It’s a self-limiting process that asymptotically approaches a steady state where the capacitor’s voltage equals the source voltage exactly. At that point dV/dt → 0, and by the governing equation, so does the current. Not approximately zero — the defining condition of “steady state” here is precisely that the voltage has stopped changing, so the current the equation predicts is exactly zero. The capacitor hasn’t become an insulator by some new mechanism; it was always an insulator, and current was only ever flowing in the wires around it while charge was still being redistributed.

AC never lets that settling finish

Apply an alternating voltage instead, and the source voltage is never constant — it’s continuously rising, falling, and reversing sign. There is no steady state for the capacitor’s voltage to settle into, because the target it’s chasing keeps moving. dV/dt never goes to zero; it oscillates, and so does the current predicted by i = C(dV/dt). The capacitor spends its entire existence mid-charge or mid-discharge, perpetually responding to a voltage that refuses to stop changing, and that perpetual response is what circuit diagrams summarise as “AC passes through.”

It’s worth being precise about where the word “blocks” comes from, since it makes the capacitor sound like a wall. It isn’t one — the governing equation never changes, for DC or AC. What changes is only whether dV/dt happens to settle at zero, and that depends entirely on whether the source lets the voltage finish settling. A capacitor in a DC circuit does let current flow, briefly, exactly as long as the voltage across it is still catching up to the source — which is the entire basis of using capacitors for timing circuits and for the brief surge current you see when switching on electronics with large capacitors across their supply rails.

The same equation also predicts the capacitor’s reactance and its 90° phase relationship between current and voltage in an AC circuit — both derived properly, with the full phasor picture, in the Alternating Current notes.