Greenhouse Energy Buffer — Interactive Physics

Capacitor voltage over timeV

SimulationAnalytic reference

Mission controls

Supercapacitor voltage during two solar power dips

Teen · coastal plant greenhouse · 75 simulated seconds

Current event

Morning lighting starts

The capacitor begins charging while supporting the lamps.

Live measurements

Playback & rendering

Your three trade-off decisions

Each can be switched during the trial. Choices affect physical results.

Experiment sliders

Moving any slider resets the run to ensure consistent measurements.

Story timeline

The science · equations & assumptions

See how capacitance, resistance, and load set RC charging times, stored energy, and voltage during interruptions.

C·dV/dt = (Vₛ−V)/Rₛ − V/Rₗ [A].

V∞ = Vₛ·Rₗ/(Rₛ+Rₗ) [V]; τ = C·Rₛ·Rₗ/(Rₛ+Rₗ) [s].

V(t) = V∞ + (V₀−V∞)·exp(−t/τ) [V] (constant source and resistances).

Stored energy E = ½·C·V² [J]; lamp power P = V²/Rₗ [W].

Assumptions & simplifications: A lumped ideal capacitor is connected in parallel with ideal resistive lamps through an ideal Thevenin source. We use a bidirectional ideal regulator model (current may flow back toward the source) and ignore diode losses, ESR, converter inefficiency, capacitance variation, and real LED current regulation. Cloud voltages are scripted illustrations, not forecasts. The backup panel has a fixed gameplay hardware-cost penalty: activating it at any time limits the score to two stars.

Graph: Solid amber is the numeric simulation; dashed cyan is the constant-conditions analytic reference. Analytic charging with the initial steady sun and unchanged load and resistance, ignoring clouds and decisions.

What you can try: Compare large and small C, switch on the backup panel before the first cloud, and see whether fast charging makes peak current exceed 3 A.

Win: Finish at 75 s with V ≥ 4.3 V and at least 48 service-weighted seconds, keeping peak absolute charger current ≤ 3 A.

Lose: Peak charger-current magnitude exceeds 3 A or final voltage/lighting service misses its threshold.

1 star: voltage ≥ 4.3 V, service score ≥ 48 s, peak current ≤ 3 A
2 stars: same constraints with service score ≥ 57 s
3 stars: same constraints with service score ≥ 64 s and without using backup hardware

Educational model · seed 391846 · no external images or fonts.

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