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On the stated $1{\mathrm{m}}^2$ area, the total electric current is $I=200\mathrm{A}$. The known ohmic polarization is $I{R}_{\Omega }=1.20\mathrm{V}$. Applying the supplied anodic Tafel equation givesAssume the quoted limiting current uses the same cathodic area convention. A steady diffusion-film model gives $c_s/c_b=1-j/j_L=1/41$. The Nernst equation then makes the cathodic concentration overpotential magnitudeRelative to the local surface equilibrium potential, the cathode also needs an activation overpotential. Neglecting anodic concentration polarization, the usual separated-loss accounting isThe printed $b$ is explicitly for copper oxidation, not a separately specified reduction slope. An exchange current density by itself does not determine the whole cathodic current-potential relation. TODO: a unique applied voltage requires a cathodic kinetic law, or an explicit additional relation between anodic and cathodic kinetics.

For a concrete conditional completion, assume one effective two-electron Butler-Volmer equation with ${\alpha }_a+{\alpha }_c=1$, no anodic concentration polarization and reduction proportional to the surface ${\mathrm{Cu}}^{2+}$ concentration. The anodic slope implies ${\alpha }_a=2.303RT/(2Fb)=0.10016$ and ${\alpha }_c=0.89984$. With $f=2F/(RT)$ and cathodic overpotential ${\eta }_c$ referenced to bulk equilibrium,Solving at $j_c=-200\mathrm{A}{\mathrm{m}}^{-2}$ gives ${\eta }_c=-0.12854\mathrm{V}$, including both concentration and activation effects. Therefore this explicitly assumed model gives $V_{\mathrm{app}}=1.20+0.67880+0.12854=2.0073$ V. The $0.04765$ V concentration loss must not be added again. A multistep copper reaction need not obey this effective single-step relation, so 2.0073 V is not uniquely entailed by the printed data.

A useful aqueous anode must deliver the desired oxidation current while limiting parasitic corrosion and hydrogen evolution. Thermodynamics sets the driving force, while activation overpotential, surface films and mass transport control the rate.

For zinc, the acid calculation favours dissolution with hydrogen evolution, but a substantial kinetic barrier to hydrogen evolution on a clean zinc surface can slow this loss. Impurities and catalytic inclusions can increase it. In alkaline electrolyte, zinc can be useful in batteries, but the unit-activity $\mathrm{Z}{\mathrm{n}}^{2+}$ calculation is incomplete: soluble zincate and zinc oxide or hydroxide alter the relevant equilibrium. A surface film can protect against corrosion or obstruct useful discharge, depending on its conductivity and transport properties.

For lead, acid corrosion has a much smaller driving force in the stipulated model, and slow hydrogen kinetics can permit practical use. The electrolyte anion matters: a lead sulfate layer in a lead–acid system has a different role from arbitrary soluble lead salts. In alkaline media, hydroxide formation, soluble complexes and passivation again need consideration before drawing a practical conclusion from the free-ion potential.

Metallic lithium is unsuitable as an exposed anode in an ordinary aqueous electrolyte. Its strongly favourable reaction with water overwhelms the argument for simply relying on a hydrogen overpotential. A lithium-ion host electrode is a different material and must be judged by its own operating potential and interfacial chemistry.

The hydrogen fuel cell is the more likely high-power choice at low temperature, for otherwise comparable electrodes, oxidant supply and device design. Similar equilibrium oxidation potentials imply similar thermodynamic voltage opportunities; they do not imply similar current densities.

Hydrogen oxidation on an appropriate catalyst is relatively facile. Ammonia oxidation requires multiple bond-breaking and nitrogen-coupling steps; adsorbed intermediates can occupy catalytic sites and inhibit continued reaction. A larger anodic activation overpotential and slower turnover reduce the useful current and operating voltage of a low-temperature ammonia cell.

Since areal power is $P/A=jV(j)$, a cell retaining substantial voltage at a larger current density can deliver more power even when its equilibrium voltage is similar. Ammonia's favorable storage characteristics are a separate system-level consideration; a comparison of power cannot be made by counting the electrons per fuel molecule alone. This is a kinetic expectation, not a universal numerical ranking independent of catalysts, temperature and transport.

At fixed discharge current, delivered voltage can be represented aswhere $Q$ is discharged charge and the terms denote distinct physical losses. A typical trace has an initial drop from open circuit, an approximately flat useful region and a final decline toward cutoff. Its exact shape depends on the cell chemistry and current; not every battery has an equally flat plateau.

Four distinguishable contributions are:

Terminology sometimes groups solid-state transport or phase-change effects differently. The important distinction is the mechanism, not counting the same diffusion loss under two names. A falling equilibrium voltage as composition changes is also not, by itself, polarization.