Electrochemistry · a showing
How a Battery Works
A battery's voltage is nothing more mysterious than the difference between two numbers on a ladder of metals. Build a cell below and watch that difference become a voltage — then meet the truth almost every explainer skips: voltage tells you next to nothing about power.
Two metals, each dipped in a solution of its own ions. One of them holds its electrons more loosely than the other. Wire them together and those electrons have somewhere to go — through your wire, doing work, instead of just sitting on the metal. That flow is the current. The whole device exists to keep the two metals apart so the electrons are forced through the long way round.
How hard does the battery push? Exactly as hard as the difference in how tightly the two metals grip their electrons. That grip has a measured number — the standard reduction potential — and the cell's voltage is just the gap between the two. Pick your metals and see.
Instrument 1 — build a galvanic cell
1.10 volts
Change the metals and the voltage changes with them — it is a subtraction, live. A Daniell cell (zinc against copper, the default) reads 1.10 V, and it reads that for one reason only: copper's potential is +0.34 V, zinc's is −0.76 V, and 0.34 − (−0.76) = 1.10. Nothing about the size of the electrodes, the amount of solution, or the thickness of the wire enters that number. Voltage is chemistry, and only chemistry.
The ladder everything hangs from
Every cell voltage above is a gap on this one scale.
Each metal sits at a height set by how badly it wants electrons. The higher a couple sits, the more it wants to be reduced (grab electrons); the lower it sits, the more readily it gives them up. Build a cell and you are simply measuring the vertical distance between two rungs.
The honest catch — you can never measure one rung
Here is the thing the tidy ladder hides: a single electrode potential cannot be measured at all. A voltmeter has two leads; it only ever reports a difference between two electrodes. So the whole ladder is pinned to an arbitrary choice — the Standard Hydrogen Electrode is defined as exactly 0 V, and every other number is measured against it. Slide the zero anywhere you like and all the cell voltages come out identical, because they are differences. The zero is a convention; the gaps are the physics.
One more true wrinkle the ladder can't show: the reactive metals at the top (lithium, sodium, magnesium, aluminium) can't sit in water as a simple electrode — they'd react with it directly. That is exactly why a lithium battery uses a non-aqueous electrolyte, and why the cell you can build above is limited to the metals that survive in water.
Voltage isn't power
The truth every explainer skips.
Ask most people what makes a car battery different from the AA in a remote and they'll say "it's more volts." It is — 12.6 against 1.5 — but that is not why one can turn a starter motor and the other can't. A lemon with a zinc nail and a copper coin makes about 0.9 V, nearly the same voltage as that AA, and it can't light a torch bulb for an instant. The voltage is a red herring.
What actually decides how much current a battery can deliver is its internal resistance — the friction the current fights inside the battery on its way out. The absolute ceiling on current is the short-circuit value I = E / Rint, and Rint is set by the battery's guts, not its voltage. Pick a battery, pick a load, and watch.
Instrument 2 — will it run the load?
The four batteries span 0.9 to 12.6 volts — a factor of about fourteen. But the current they can deliver spans from under a milliamp to well over a thousand amps: a factor of more than a million. That entire spread lives in the internal resistance, not the voltage. To feel it directly, hold the voltage fixed and move only the resistance:
Instrument 3 — a fixed 2.0-volt source, varying only Rint
The voltage never moves. The current does everything.
That is the whole secret of battery design. Making a high voltage is easy — pick reactive chemistry, or stack cells in series (a 12-volt car battery is six 2-volt lead-acid cells in a row). Making a battery that can dump hundreds of amps without its voltage collapsing is the hard, engineered part: thin separators, huge electrode areas, low-resistance everything. Voltage is what the chemistry gives you for free. Power is what the engineering earns.
The check
Every cell voltage this page shows is recomputed, live, as
E°(cathode) − E°(anode) from a single tabulated ladder of standard
reduction potentials (CRC Handbook / IUPAC values, 25 °C, vs the Standard
Hydrogen Electrode). The verifier
research/how-a-battery-works/verify.mjs reproduces the ladder to
within 0.02 V of the literature, and from it the canonical cells:
Daniell = 1.10 V, silver–zinc = 1.56 V, one
lead-acid cell = 2.04 V (×6 = 12.24 V). It also checks
the thermodynamics — ΔG° = −nFE° gives −212 kJ/mol for the
Daniell cell — and the Nernst slope, RT·ln10/F = 59 mV per
decade (that 59 mV holds only at 25 °C; the slope scales with
temperature).
Standard vs. real, on the car battery. The 2.04 V per lead-acid cell (→ 12.24 V for six) is the standard-state EMF, at 1 M acid. A real fully-charged cell runs on concentrated acid, and the Nernst term lifts its resting voltage to about 2.1 V — which is why a healthy 12 V battery reads ~12.6 V at rest, the figure Instrument 2 uses. Fe²⁺/Fe is shown at its classic textbook −0.44 V; modern CRC tables list −0.447 V (which rounds to −0.45).
Exact vs typical, stated plainly. The cell voltages and constants
are exact — derived here from tabulated potentials. The internal
resistances and currents in Instruments 2 and 3 (lemon ≈ 1 kΩ, AA
≈ 0.2 Ω, coin cell ≈ 10 Ω, car ≈ 8 mΩ; LED ≈ 15 mA, starter
≈ 150 A) are typical, order-of-magnitude figures — real devices vary
with construction, charge, and temperature. The verifier checks only the model's
arithmetic (I = E/(R_int+R_load)) and the qualitative verdicts, and
the page labels these numbers as approximate wherever they appear.