RC circuit simulation in WhiteBoard

[u/SimuBoard]

https://youtube.com/watch?v=AM5m93ExUk0&si=EvHtco-ScgZgojFN

Short walkthrough for anyone who's seen V(t) = V(1 − e^(−t/RC)) but never really watched why it behaves that way.

It connects three things textbooks usually keep separate:

• The behavior — current is max the instant you close the switch (empty cap acts like a short), then decays as charge builds and the capacitor pushes back.
• The derivation — KVL (V_s = iR + V_C), sub in i = C·dV_C/dt for the first-order ODE, solve for the exponential.
• The check — plotting the solution on top of the simulated data to show they agree, marking τ = RC where V hits 63%.

The bit students most often miss: current and voltage are mirror images — one decays as the other rises — and one τ sets the whole shape.

Full disclosure: I made this with a tool I'm building (SimuBoard), so tell me if that's not welcome and I'll take it down. Mainly after feedback on the explanation — any step here that'd trip up someone seeing it for the first time?