Circuit Builder Teaser

The brief

Create a single-file HTML/Canvas page that lets the user adjust $R$, $L$, $C$ values and plots the step response of a series RLC circuit in real time.

The step response of a series RLC circuit is governed by a second-order linear ODE. The model must classify the damping regime, choose an appropriate numeric method, and keep the plot readable as parameters sweep across orders of magnitude.

What a strong output looks like

• Derivation or clear statement of the governing equation:

$L \frac{d^2i}{dt^2} + R \frac{di}{dt} + \frac{1}{C} i = \frac{V_s}{L}$

• Damping classification using $\alpha = R/2L$ and $\omega_0 = 1/\sqrt{LC}$:
  • underdamped when $\alpha < \omega_0$,
  • critically damped when $\alpha = \omega_0$,
  • overdamped when $\alpha > \omega_0$.
• Adaptive or small fixed time step to keep the solver stable.
• Log-scaled or normalised sliders that handle ranges from milliohms to kiloohms and microhenries to henries.
• Clear axis labels and a live regime indicator.

Scoring notes

• 40% damping classification: the displayed regime matches the chosen parameters.
• 30% solver stability — no divergence, ringing artifacts from the integrator itself, or NaN values.
• 20% usability — sliders are labelled, the plot auto-scales, and the curve is readable.
• 10% explanation — the page or code explains the physics in terms a reader can follow.