Supercapacitor Charge-Discharge Cycling

Cycling Parameters

Charge/discharge current I 0.50 A

Double-layer capacitance C 1.00 F

Equivalent series resistance (ESR) 80 mΩ

Live Readout

CHARGING

Terminal voltage V

0.00 V

Stored energy ½CV²

0.00 J

Charge Q = CV

0.00 C

Cycle count

How it works

An electric double-layer capacitor (EDLC / supercapacitor) stores charge electrostatically, not chemically: applying a voltage pulls electrolyte ions of the opposite charge onto each porous carbon electrode's surface, forming a nanometre-thick Helmholtz double layer instead of driving a redox reaction. Because no chemical bond breaks or forms, cycling is extremely fast and largely reversible.

Double-layer capacitance:  C = ε₀εᵣA / d
  ε₀εᵣ = electrolyte permittivity, A = electrode surface area,
  d = separation between the ion plane and the electrode surface (~0.3-0.5 nm)

Galvanostatic charge:      V(t) = I·R_ESR + (I/C)·t
Galvanostatic discharge:   V(t) = V₀ − I·R_ESR − (I/C)·t
Stored energy:             E = ½CV²          Charge:  Q = CV

Current I — the constant charge/discharge current. A higher I ramps voltage faster (steeper V-t slope = I/C) but wastes more energy as I²R_ESR heat.
Capacitance C — stands in for the electrode's usable surface area/porosity. A bigger C (more surface area) charges to the same voltage more slowly for a given current, and stores more energy per volt.
ESR — internal resistance of electrolyte + electrode + contacts. It causes the instantaneous voltage "jump" (IR drop) visible the moment the current direction reverses — the classic signature that separates a real supercapacitor's triangular V-t trace from an ideal one.

In the 3D view, blue cations drift toward the negative electrode and red anions toward the positive electrode as voltage rises, hugging the electrode surface to form the double layer; on discharge they relax back into the bulk electrolyte. This is the same galvanostatic charge-discharge (GCD) test used in real labs to measure a supercapacitor's capacitance, ESR and energy density.

Cation (+) Anion (-) Porous carbon electrode

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