RC circuits: capacitors remember

A capacitor stores charge. The moment you connect it to a voltage source through a resistor, it starts to fill up — and the fill-up curve has a specific, beautiful shape.

The circuit

V ──[ R ]──┬──[ C ]── GND
           │
         V_cap

Close the switch. V_cap starts at 0V and climbs toward V. The time constant is:

τ = R × C

• τ (tau) is in seconds when R is in ohms and C is in farads.
• After 1τ the cap is at 63% of the target voltage.
• After 3τ it's at 95%. We call this "basically full".
• After 5τ it's at 99%.

The math

V_cap(t) = V × (1 − e^(−t/τ))

The exponential. Same curve as population growth, cooling coffee, radioactive decay (running in reverse). Once you see it in one place, you see it everywhere.

Try it

@exosynk/rc-lowpass has a 9V battery, 10kΩ resistor, and a 100μF capacitor.

• τ = 10,000 × 0.0001 = 1 second
• Open the oscilloscope (shortcut: press O or use the toolbar)
• Probe V_cap
• Press the simulate button. You'll see the exponential rise exactly as drawn above — ExoSynk's transient sim is real math, not a look-up.

Why this matters

Every button on your keyboard has an RC debounce somewhere. Every audio filter has RC-shaped cutoff. Every Arduino analog pin takes ~100 μs to stabilize after a read because of an RC at the input.

Once you're comfortable reading an RC curve, a huge chunk of "real" electronics becomes legible.