ENERGY

From farads to watt-hours

Wh = ½ C V² / 3600

Energy in joules is ½CV². To quote it in watt-hours, divide by 3600. Then divide by mass, volume, or area to get an energy density in Wh/kg, Wh/L, or µWh/cm².

Energy density needs both a numerator and a denominator.

POWER

Maximum versus average

P_max = V² / (4 · ESR)

Maximum power depends on the voltage squared and the ESR, as in Part 5. Average power from a discharge is simply the energy delivered divided by the discharge time. Papers use both, so check which one is being quoted.

A wide voltage window and a low ESR both push power up.

WHICH DENOMINATOR

Normalize to what matters

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Gravimetric

Per gram: F/g, Wh/kg. Common for bulk cells and material studies

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Volumetric

Per cm³: F/cm³, Wh/L. Matters when space is tight

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Areal

Per cm² of footprint: mF/cm², µWh/cm². Matters for on-chip micro devices

Pick the denominator that matches the constraint of the application.

NORMALIZATION TRAPS

How good numbers get inflated

Active material only Ignores collectors, separator, electrolyte, and packaging, so a real device looks worse

Thin films A tiny active mass makes per-gram values look huge, so quote area or volume instead

Single electrode vs. device Remember the factor of four from the first unit of this part

Mixed units F/g, mF/cm², and F/cm³ cannot be compared with each other

A number without its denominator is not a result.

BUILDING A RAGONE PLOT

From charge–discharge to a curve

each current → a point

Run GCD at several currents. At each one, compute energy density and power density. Plot energy against power on log–log axes, one point per current. Higher current gives higher power but lower energy, tracing the tradeoff from Part 1's Ragone plot for your own device.

A Ragone curve shows what a device does across its whole operating range, not at one favorable point.

UNIT 29 STUDY COMPLETE

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Ready for the Fab Challenge?

You've covered turning data into Wh, W, and Ragone points, per gram, per cm², or per cm³.