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9.3 — Batteries: Chemistry to Charge Cycles
A battery converts chemical energy directly into electrical energy, with no combustion and no moving parts. Alessandro Volta built the first one around 1800 by stacking zinc and copper discs separated by brine-soaked cloth, and the principle has not changed.
What has changed is everything about the numbers, and the last thirty years of change in that one component is why phones, laptops and electric cars exist.
A battery is chemistry doing the job that Chapter 9.1's transformer does electrically: supplying a voltage. The reactions below are the electrochemistry of Volume IV Chapter 10.5, and the voltage a cell produces is decided there, not by anything an engineer can choose.
1. How a cell works
Three parts:
- Anode — where oxidation happens, releasing electrons.
- Cathode — where reduction happens, consuming electrons.
- Electrolyte — conducts ions between them but not electrons.
That last clause is the whole design. The electrolyte forces the electrons to travel through the external circuit instead of taking a short cut inside the cell, and that journey is where the work gets done.
In a lithium-ion cell:
\text{Discharge: } \text{LiC}_6 \to \text{Li}^+ + e^- + \text{C}_6 \quad\text{(anode)}
\text{Li}^+ + e^- + \text{CoO}_2 \to \text{LiCoO}_2 \quad\text{(cathode)}
Lithium ions travel through the electrolyte and electrons travel through your device. Charging reverses both.
Nothing is consumed and nothing is plated out. The lithium ions simply move back and forth, sliding into and out of the layered structures of the graphite and the oxide. This is called intercalation, and it is why lithium-ion cells last for hundreds of cycles where earlier chemistries degraded rapidly — the electrodes are not being dissolved and rebuilt, only filled and emptied.
Cell voltage comes from the difference in the two electrodes' electrochemical potentials, and it is a property of the chemistry, not of the size:
| Chemistry | Nominal voltage |
|---|---|
| Zinc-carbon | 1.5 V |
| Alkaline | 1.5 V |
| NiMH | 1.2 V |
| Lead-acid | 2.0 V |
| Lithium-ion (LCO) | 3.7 V |
| LiFePO4 | 3.2 V |
| Lithium primary | 3.0 V |
A bigger cell of the same chemistry has the same voltage and more capacity. A D cell and an AAA cell are both 1.5 V; the D holds twenty times the charge.
2. The numbers that matter
Capacity, in amp-hours:
Q=\int I\,dt
But amp-hours alone are meaningless across chemistries, because the voltages differ. Watt-hours is the honest comparison:
E=Q\times V_{avg}
Worked example. A 3000 mAh lithium cell at 3.7 V:
E=3\times3.7=11.1\ \text{Wh}
A 3000 mAh NiMH cell at 1.2 V holds only 3.6 Wh — a third as much, despite the identical amp-hour rating. This is why phone batteries are quoted in mAh and power banks are increasingly quoted in Wh, and why comparing a power bank's mAh rating with a phone's is meaningless unless both voltages are stated.
C-rate expresses current relative to capacity:
\text{C-rate}=\frac{I}{Q}
A 2000 mAh cell at 1C is 2 A; at 0.5C it is 1 A and lasts two hours; at 5C it is 10 A and lasts twelve minutes.
Energy density, in two forms that matter for different reasons:
\text{gravimetric}=\frac{\text{Wh}}{\text{kg}}, \qquad \text{volumetric}=\frac{\text{Wh}}{\text{L}}
| Chemistry | Wh/kg | Wh/L |
|---|---|---|
| Lead-acid | 35 | 80 |
| NiCd | 50 | 100 |
| NiMH | 90 | 250 |
| Li-ion (LCO) | 200 | 550 |
| Li-ion (NMC) | 250 | 700 |
| LiFePO4 | 130 | 300 |
| Petrol, for comparison | 12,000 | 9,000 |
Petrol holds fifty times more energy per kilogram than the best battery. That number, more than any other, explains why electrification of transport took so long and why aviation remains hard.
The counter-argument, which is real: an electric motor is 90% efficient where an internal combustion engine is 25%. So the usable energy ratio is nearer 14:1 than 50:1, and a battery pack does not need a gearbox, an exhaust, a cooling system or a fuel tank. For a car that is enough; for an airliner it is not.
3. The chemistries
Primary — not rechargeable
Zinc-carbon. The cheapest possible cell, poor at high current, and prone to leaking as the zinc case is consumed. Largely obsolete.
Alkaline. Zinc powder and manganese dioxide in potassium hydroxide. Five to ten times the capacity of zinc-carbon at moderate currents, ten-year shelf life, and it is what almost every household AA cell is.
Lithium primary (Li-MnO2). 3 V, excellent at low temperature, ten to twenty years of shelf life with under 1% self-discharge per year. This is what a coin cell in a smoke alarm or a memory backup is, and the long shelf life is the reason.
Secondary — rechargeable
Lead-acid, 1859. The oldest rechargeable chemistry still in mass use, and it survives for three specific reasons: it is cheap, it delivers enormous current, and it is almost universally recycled — over 95% of lead-acid batteries are recycled, the highest rate of any consumer product.
Its enormous current capability is why it starts cars. A starter motor draws 200 to 400 A, which no other affordable chemistry supplies from that size.
Its weakness is depth of discharge. A car battery discharged below 50% repeatedly will fail within months, because the lead sulphate crystals formed during discharge grow and become hard to reconvert — a process called sulphation. A deep-cycle battery is built with thicker plates specifically to survive it, at the cost of lower peak current.
NiCd. Robust, tolerant of abuse, works at -40 °C, and contains cadmium, which is severely toxic and now restricted almost everywhere.
The famous "memory effect" is largely a myth. True memory — a voltage depression from repeated identical partial discharges — was a real but narrow phenomenon in spacecraft cells. What most people experienced was voltage depression from overcharging, which is reversible.
NiMH. Replaced NiCd with double the capacity and no cadmium. Its historical flaw was self-discharge of 20 to 30% per month, making it useless for a device left in a drawer.
Low self-discharge NiMH, from 2005, cut that to about 15% per year, and it is what a rechargeable AA now is — genuinely useful for remote controls and clocks in a way its predecessors were not.
Lithium-ion. The chemistry that changed portable electronics, and the cathode material determines its character entirely:
| Cathode | Wh/kg | Cycles | Character |
|---|---|---|---|
| LCO (cobalt) | 200 | 500 | highest energy, least safe |
| NMC (nickel-manganese-cobalt) | 250 | 2000 | the modern balance |
| LFP (iron phosphate) | 130 | 5000+ | safest, longest life, heaviest |
| NCA (nickel-cobalt-aluminium) | 260 | 1000 | high energy, used in EVs |
| LTO (titanate anode) | 80 | 20,000 | very fast charge, very long life |
LFP is now taking a large share of electric vehicle production, and the reasoning is worth understanding: it holds 40% less energy per kilogram, and it lasts four times as many cycles, is far safer, contains no cobalt, and can be routinely charged to 100% without damage — which recovers much of the range difference in practice, because an NMC pack is deliberately never fully charged.
4. The discharge curve
A battery is not a voltage source with a series resistor. Its voltage falls as it discharges, and the shape of that fall is chemistry-specific and consequential.
Lithium-ion NMC runs from 4.2 V charged to 3.0 V empty, with a usable slope. Voltage gives a rough state of charge, and that is how most phones estimate it.
LiFePO4 sits at 3.2 to 3.3 V across nearly the entire discharge. Voltage tells you almost nothing about state of charge, so an LFP system must use coulomb counting — integrating current in and out — with periodic recalibration at the ends.
Alkaline falls steadily from 1.5 V to 0.9 V, which is why a device must work across that whole range and why a "dead" alkaline cell still measures over 1 V under no load.
The knee is where the voltage collapses. Past it there is essentially nothing left, and a device that keeps drawing current there simply damages the cell.
Internal resistance rises with age and falls with temperature:
V_{terminal}=V_{OCV}-I\,R_{internal}
Worked example. A phone battery with 100 mΩ internal resistance drawing 2 A during a camera flash:
\Delta V=2\times0.1=0.2\ \text{V}
A cell at 3.4 V drops to 3.2 V for the duration.
And this is exactly why an old phone shuts down suddenly at 30% charge. The internal resistance has risen to perhaps 400 mΩ, so a burst of load drops the terminal voltage below the cutoff, and the phone shuts down even though charge remains. Apple's 2017 controversy over throttling old phones was this problem: the software reduced peak processor demand to keep the current low enough to avoid the shutdown.
5. Charging lithium safely
Lithium cells are the only common chemistry where incorrect charging is genuinely dangerous, and the protocol exists entirely to prevent that.
CC-CV — constant current, then constant voltage:
Phase 1 — trickle. If the cell is below about 3.0 V, charge at 0.1C until it recovers. A deeply discharged cell charged at full current can plate metallic lithium, which forms dendrites that eventually pierce the separator and short the cell internally.
Phase 2 — constant current at 0.5C to 1C, until the voltage reaches 4.2 V. This delivers about 70% of the capacity.
Phase 3 — constant voltage at 4.2 V, with the current falling as the cell fills. Stop when the current falls below about 0.05C. This phase takes as long as the previous one for the last 30%.
Which is why charging is fast to 80% and slow after. The constant-current phase is quick; the constant-voltage tail is not, and it cannot be shortened without damage.
The hard limits, and each has a specific consequence:
Never exceed 4.2 V per cell. Overcharging drives lithium plating and oxygen release from the cathode, leading to thermal runaway.
Never discharge below 2.5 V. The copper current collector begins to dissolve, and on recharge the dissolved copper redeposits as internal shorts. A cell taken below about 2.0 V should be discarded, not revived.
Never charge below 0 °C. At low temperature the graphite cannot accept lithium fast enough and it plates on the surface instead. This is permanent damage and a safety hazard, and it is why an electric car preheats its pack before fast charging in winter, and why a phone left in a cold car refuses to charge.
Balance cells in series. Cells age at slightly different rates, so without balancing one cell reaches 4.2 V while others are still at 4.0 V. Continue charging and that cell is overcharged. A battery management system either bleeds charge from the highest cell through a resistor (passive balancing) or transfers it to the lowest (active balancing).
Fast charging, honestly
Higher current alone does not work, because I^2R heating and lithium plating both limit it.
The techniques that actually enable it:
- Higher voltage delivery — 20 V instead of 5 V at the same current, so four times the power through the same cable. This is what USB Power Delivery does.
- Split-cell packs charged in parallel at lower current each.
- Active cooling during charge.
- Temperature-aware tapering — reduce current as the cell warms.
The cost is cycle life. Charging at 3C rather than 0.5C typically halves the number of cycles a cell survives. Every fast-charging system is trading longevity for convenience, and the manufacturers that let you limit charging to 80% are offering you the other side of that trade.
6. Ageing
Two distinct mechanisms, and it is worth separating them because they respond to different things.
Calendar ageing happens whether or not the battery is used. The solid electrolyte interphase layer on the anode thickens over time, consuming lithium and raising internal resistance.
It is accelerated by high state of charge and high temperature. Rough figures for annual capacity loss:
| Storage | Loss per year |
|---|---|
| 40% charge, 0 °C | 2% |
| 40% charge, 25 °C | 4% |
| 100% charge, 25 °C | 20% |
| 100% charge, 40 °C | 35% |
A laptop left permanently plugged in at 100% and running warm loses a third of its capacity a year. This is why laptops and phones now offer to hold the charge at 80%, and it is a genuinely significant feature rather than a marketing one.
Cycle ageing comes from the mechanical stress of expansion and contraction during charge and discharge, which cracks electrode particles.
Depth of discharge dominates it:
| Depth of discharge | Cycles to 80% capacity |
|---|---|
| 100% | 500 |
| 80% | 1,000 |
| 50% | 3,000 |
| 20% | 15,000 |
Read the total energy delivered, not the cycle count. 500 full cycles delivers 500 pack-equivalents; 3000 half cycles delivers 1500. Shallow cycling delivers three times more total energy from the same cell, which is why grid storage systems and electric vehicles deliberately restrict the usable range.
An electric car's "100%" is typically 90% of the true capacity, and its "0%" is around 10% — and that hidden buffer is why a car's battery lasts far longer than a phone's despite the same chemistry.
7. The battery management system
Any pack of more than one cell needs one, and it does five things.
Protection — cut off on overvoltage, undervoltage, overcurrent, short circuit and over- or under-temperature. Every one of these is a safety function, not a convenience.
Balancing — keep the cells within a few millivolts.
State of charge estimation — usually a Kalman filter (Chapter 6.7) combining coulomb counting, which is accurate over short periods but drifts, with voltage measurement, which is noisy but has no drift. The filter uses each to correct the other's weakness, which is exactly what a Kalman filter is for.
State of health estimation — tracking capacity fade and internal resistance rise to predict remaining life.
Thermal management — heaters, fans or liquid cooling, holding the pack in the 15 to 35 °C band where both performance and longevity are best.
Thermal runaway is what the BMS exists to prevent. Above about 130 °C the separator melts, the electrodes touch, and the resulting short generates more heat. Above 200 °C the cathode releases oxygen, which feeds a fire that cannot be extinguished by removing air, because the battery supplies its own oxidiser.
And it propagates. One cell in runaway heats its neighbours until they follow. Pack design therefore focuses on preventing propagation: physical spacing, fire-resistant barriers between cells, and vents that direct hot gas away from adjacent cells rather than into them.
Every formula above, built from scratch
None of the results in this chapter are worth memorising, because each one can be rebuilt in under a minute from something simpler. What follows is that rebuilding, one result at a time, so the formula and the reason for it sit on the same page as the explanation that needed them.
Batteries
Q=\int I\,dt \ \text{(Ah)}, \qquad E=Q\times V_{avg} \ \text{(Wh)}
Watt-hours is the only honest comparison across chemistries, since amp-hours ignores the voltage.
\text{C-rate}=\frac{I}{Q}
V_{terminal}=V_{OCV}-I\,R_{internal}
Worked: 2 A through 100 mΩ drops 0.2 V; through an aged 400 mΩ cell it drops 0.8 V, which is why old phones shut down at 30%.
Energy densities:
| Chemistry | Wh/kg |
|---|---|
| Lead-acid | 35 |
| NiMH | 90 |
| LFP | 130 |
| Li-ion NMC | 250 |
| Petrol | 12,000 |
The 50:1 ratio to petrol falls to about 14:1 once the motor's 90% efficiency is set against an engine's 25%.
Peukert's law, for lead-acid capacity at high current:
t=\frac{H}{(I/I_H)^{k}}, \qquad k\approx1.1\text{–}1.3
Charging: CC-CV. Trickle below 3.0 V at 0.1C; constant current at 0.5–1C to 4.2 V; constant voltage until the current falls below 0.05C.
Ageing. Calendar loss roughly doubles per 10 °C and is far worse at high state of charge — 4% a year at 40% charge and 25 °C, against 20% at 100% charge.
Cycle life against depth of discharge:
| DoD | Cycles to 80% |
|---|---|
| 100% | 500 |
| 50% | 3,000 |
| 20% | 15,000 |
Total energy delivered is what matters, and 3000 half-cycles delivers three times what 500 full ones do.
8. What comes next
Solid-state. Replace the liquid electrolyte with a solid one. Non-flammable, potentially enabling a pure lithium metal anode with much higher capacity, and possibly faster charging. The obstacles are real: manufacturing large defect-free solid electrolyte sheets, maintaining contact as the electrodes change volume during cycling, and cost. Predicted for a decade and still not in volume production.
Sodium-ion. Sodium is abundant and cheap where lithium is not. Lower energy density, and genuinely viable for grid storage where weight does not matter. Already in production in China.
Lithium-sulphur. Theoretically five times the energy density. Cycle life is the unsolved problem — the sulphur cathode dissolves into the electrolyte over cycling.
And the honest assessment. Lithium-ion energy density has improved by roughly 5 to 8% per year for thirty years, and cost has fallen by about 90% since 2010. That steady incremental improvement has been worth more than any of the announced breakthroughs, and it is what actually made electric vehicles competitive. A technology that improves reliably at 6% a year doubles every twelve years, and that is a hard thing to displace.
Chapter 9.4 uses the transformer principle of Chapter 9.1 across an air gap, to charge a battery through a case with no connector at all.
What the next chapter fixes
Charging a battery normally means plugging it in. Chapter 9.4 covers doing it without contacts, which is the transformer of Chapter 9.1 with its iron core removed — and shows what that removal costs and the one trick that partly recovers it.