Cell Voltage
Part of Energy Storage & Batteries
Cell voltage is determined by the chemical potential difference between electrode materials — understanding it lets you design batteries for any target voltage.
Why This Matters
Every battery chemistry produces a characteristic voltage. A zinc-copper cell produces about 1.1 V. A lead-acid cell produces 2.0 V. A carbon-zinc cell produces 1.5 V. These voltages are not arbitrary — they are determined by the thermodynamic difference in chemical potential between the oxidation and reduction reactions at each electrode. This is fundamental physics that you cannot change by adjusting construction, only by changing the chemistry.
Understanding cell voltage matters practically because most electrical loads require specific voltage ranges. A 12 V system needs exactly 6 lead-acid cells in series. A 6 V flashlight needs 4 carbon-zinc cells. Getting the voltage wrong by even a factor of two can damage equipment or deliver inadequate power. Knowing where these voltages come from lets you predict, design, and troubleshoot battery systems systematically.
For a rebuilding civilization, the ability to design battery stacks to specific voltages — and understand why they behave as they do under load — is the difference between a battery system that works reliably and one that fails unpredictably.
Half-Cell Potentials
The voltage of a cell comes from combining two half-reactions: oxidation at the anode and reduction at the cathode. Each half-reaction has a characteristic potential measured against a standard hydrogen electrode (defined as 0.00 V).
Standard electrode potentials (selected values):
- Li⁺/Li: −3.04 V (very reducing — high potential as anode)
- Zn²⁺/Zn: −0.76 V
- Fe²⁺/Fe: −0.44 V
- Ni²⁺/Ni: −0.23 V
- H⁺/H₂: 0.00 V (reference)
- Cu²⁺/Cu: +0.34 V
- Ag⁺/Ag: +0.80 V
- MnO₂/Mn²⁺: +1.23 V (approximate, varies with conditions)
- PbO₂/PbSO₄: +1.69 V
Cell voltage calculation: E_cell = E_cathode − E_anode (both measured as reduction potentials). For a zinc-copper cell: E = +0.34 − (−0.76) = 1.10 V. For lead-acid: E = +1.69 − (−0.36) = approximately 2.05 V.
These are standard potentials under ideal conditions (25°C, 1 M concentration, 1 atm). Actual cell voltages differ somewhat based on temperature, concentration, and electrode surface condition.
Open-Circuit Voltage vs. Working Voltage
Open-circuit voltage (OCV): The voltage measured with no current flowing. This reflects the true thermodynamic potential difference and is always the highest voltage the cell can produce.
Working voltage: Voltage under load — always lower than OCV. The difference is caused by:
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Internal resistance (IR drop): Current flowing through the electrolyte and electrode materials causes a voltage drop proportional to current (V = IR). Higher current → larger drop → lower terminal voltage.
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Concentration polarization: As reaction proceeds, reactant concentrations at the electrode surface change (depleted reactants, accumulated products), shifting the effective electrode potential.
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Activation overpotential: Starting a reaction requires extra energy beyond the thermodynamic minimum — a kinetic barrier. This is why practical electrolyzers need ~1.8 V even though thermodynamics requires only 1.23 V to split water.
Voltage under load: V_terminal = E_cell − I × R_internal. For a lead-acid cell with R_internal = 0.05 Ω, drawing 10 A: V = 2.05 − (10 × 0.05) = 1.55 V per cell. Under 100 A: V = 2.05 − 5 = essentially zero (short circuit current).
Series and Parallel Stacking
Series connection: Connects positive terminal of one cell to negative terminal of the next. Voltages add; capacity stays the same. Four 1.5 V cells in series = 6 V total at the same milliampere-hour rating as one cell.
Parallel connection: Connects all positives together, all negatives together. Voltage stays the same; capacity multiplies. Four 1.5 V cells in parallel = 1.5 V at four times the capacity.
Series-parallel combinations: A 12 V, 100 Ah lead-acid bank from 2 V cells needs 6 cells in series × however many strings in parallel for capacity. Six cells in series = 12 V; 5 parallel strings of 6 = 12 V at 5× capacity.
Balancing cells in parallel: Cells in parallel must have the same voltage or the higher-voltage cell will charge the lower. This is acceptable during normal operation but can damage cells that develop different discharge characteristics. Always use cells of the same type, age, and condition in parallel.
Measuring and Monitoring Cell Voltage
Voltmeter use: A good voltmeter draws negligible current and reads OCV accurately. Measure each cell individually to identify weak cells in a series string — a weak cell shows lower voltage and causes disproportionate capacity reduction.
Load testing: OCV alone can be misleading. A partially discharged lead-acid cell may show 12.5 V open-circuit but collapse to 10 V under a 10 A load. Load test with a known resistance and observe voltage under load for 30 seconds.
State of charge indicators:
- Lead-acid: 12.7 V (100%), 12.4 V (75%), 12.2 V (50%), 12.0 V (25%), 11.8 V (discharged)
- Carbon-zinc: 1.55 V (fresh), 1.3 V (50% used), 1.1 V (nearly exhausted)
- Nickel-iron: 1.2 V (full), 1.0 V (discharged), 0.8 V (over-discharged, harmful)
Temperature effects: All cell voltages decrease slightly with falling temperature. Lead-acid capacity drops ~20% at 0°C. Lithium chemistry is especially sensitive to low temperatures. For cold-climate operation, insulate battery banks and monitor voltage more carefully in winter.
Understanding cell voltage at this level — from half-cell potentials through stack design to load testing — gives you the ability to design battery systems from scratch and diagnose problems when they arise.