THE CORE EQUATION

What sets capacitance

C = εA / d

Capacitance (C) depends on the permittivity of the dielectric (ε), the electrode surface area (A), and the separation distance between electrodes (d). Bigger area or a smaller gap both raise capacitance.

Key idea Every strategy for a better supercapacitor electrode — more surface area, tighter spacing — traces back to this one equation.

CHARGE, VOLTAGE, ENERGY

From capacitance to energy

Capacitance C = ratio of stored charge to applied voltage

Stored energy E = ½ · C · (ΔV)²

Energy scales with voltage squared — small increases in operating voltage window matter a lot for how much energy a device can hold.

THINKING IN AREA

Why "areal" matters here

Micro supercapacitors don't have the luxury of scaling up — their footprint is fixed by the device they're powering. So instead of measuring performance per gram, this field measures performance per unit area: areal charge storage (mC/cm²), areal capacitance (mF/cm²), and areal energy density.

Q_A = (1/vA) ∫|I(V)| dV · C_A = Q_A / ΔV

Areal charge storage is calculated from the area inside a cyclic voltammogram (CV) curve — you'll see CV curves throughout this course.

LEVERS YOU CAN PULL

Four ways to raise capacitance

More surface area

Bigger electrode area, same footprint

Less spacing

Shorter distance between electrode fingers

Better electrolyte transport

Ions reach the electrode surface faster

Reversible redox reactions

Add faradaic charge storage on top of electrostatics

Every device design choice later in this course — electrode geometry, electrode height, electrolyte choice — is really just pulling one of these four levers.

UNIT 3 STUDY COMPLETE

⚡

Ready for the Fab Challenge?

You've covered the core equations behind how much charge and energy an electrode can store.