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An electric battery converts the available chemical Gibbs free energy of one or more galvanic cells into electrical work delivered to an electrical load. The reacting materials are a finite reservoir: a battery can sustain a terminal electric potential difference while discharging, but cannot supply energy indefinitely. Unlike a capacitor, whose capacitor energy resides in an electric field, a battery chiefly stores its available energy in the chemical state of its materials. The detailed half-reactions and apparatus of a Daniell cell explain this conversion at the electrode level.

During discharge, electrons move through metallic wires from the negative anode, through the electrical load, to the positive cathode; external conventional current points the other way. Inside the battery, ions carry electric current through the electrolyte, and redox chemical reactions connect ionic transport to electronic transport at the electrodes. The same electron does not make a lap through both wire and electrolyte. Electric charge conservation closes the circuit; changing chemical composition supplies the energy. See galvanic cell for the two transport paths and electrolyte for how oppositely moving ions contribute to one net electric current.

The source's electromotive force $\mathcal{E}$ measures its driving work per unit electric charge, in volts; the loaded terminal electric potential difference $V_L$ measures the electrical work per unit electric charge delivered outside the battery. They agree in an ideal lossless source, or approximately near open circuit, but generally differ during discharge.^[ref]

In the ideal fixed-voltage model used in fixed-voltage capacitor energy balance, a battery maintains a prescribed terminal electric potential difference while electric charge flows to or from the capacitor. This is a constraint for that calculation, not an inexhaustible reservoir. The fixed-voltage capacitor energy balance also accounts for electrical energy returned to the source; an actual cell can accept sustained charging only if its chemistry and operating conditions permit it.

An ordinary capacitor stores energy by separating charge across a dielectric: $E=C{V}^2/2$ and $Q=CV$. Electronic charge redistribution is rapid, giving high specific power, but the dielectric breakdown field and modest capacitance limit specific energy. Series resistance limits pulse power and produces heating; a large nominal capacitance does not remove those losses.

A supercapacitor has a much larger interfacial area and nanometre-scale charge separation. An electric double-layer capacitor stores charge without a bulk redox transformation; pseudocapacitance adds sufficiently fast surface or near-surface redox storage. ion motion in pores, electrolyte stability and series resistance constrain its response. Its specific energy usually exceeds an ordinary capacitor's while high specific power and cycling durability remain possible.

An electric battery stores chemical free energy through coupled electrode oxidation-reduction reactions. It can store substantial energy per mass, but charge transfer, ionic transport, diffusion and heat removal constrain rapid discharge. The terminal voltage and accessible capacity depend on discharge rate and state of charge. Accordingly the plotted order follows the storage and transport mechanisms; it is not a claim that every battery has less power than every supercapacitor.

In a galvanic cell, a spontaneous oxidation-reduction reaction supplies electrical work: ${\Delta }_{r}G<0$ for discharge, the anode is negative, and the cathode positive. A discharging electric battery and a hydrogen–oxygen fuel cell are two practical examples. The first stores its reactants internally; the second is supplied continuously with fuel and oxidant.

An electrolytic cell consumes externally supplied electrical work to drive electrode reactions or material transfer under an applied potential. Its anode is positive and cathode negative. water electrolysis for hydrogen production and metal electroplating are two practical examples. oxidation always occurs at the anode and reduction at the cathode in both cell types; the electrode signs change. The electrolyte conducts ions, while electrons flow through the external circuit. A rechargeable battery can operate in either regime depending on whether it is discharging or being charged.

Use the parallel-plate capacitor approximation, neglecting the fringing field of a capacitor. With plate area $A=\pi (0.10\mathrm{m}{)}^2$, the initial capacitance and opposite plate electric charges areAfter the electric battery is disconnected, the isolated plate electric charges stay fixed. Doubling the separation halves the capacitance. The quasistatic pulling work is the increase of electrostatic energy:The final electric potential difference is thereforeAn electron released at rest gains kinetic energy $e\Delta V_f$, where $e$ is the positive elementary charge. Neglecting radiation and the negligible perturbation caused by this one electron, conservation of energy givesThis is $0.0280c$, so the nonrelativistic kinetic energy is adequate. The circular plates have finite radii; the numerical results are leading parallel-plate capacitor values rather than exact finite-plate capacitances.

The original diagram has an ideal $5\mathrm{V}$ electric battery feeding series resistors of $8\Omega$ above the tapping point and $2\Omega$ below it. The long battery bar is positive, so terminal $A$ is above terminal $B$ in electric potential. With an open circuit at the output, the internal electric current is $5/(8+2)=0.5\mathrm{A}$. The voltage divider therefore givesFor the Thévenin resistance, suppress the ideal voltage source by replacing it with a short circuit. The two resistors are then in parallel as seen from $A,B$:By Thévenin's theorem, the terminal voltage under an outward load electric current $I$ is $V_A-V_B={\mathcal{E}}_0-I{R}_{\mathrm{Th}}$. Consequentlyflowing through an external short circuit from $A$ to $B$. Directly shorting the original terminals bypasses the $2\Omega$ resistor and leaves $5\mathrm{V}$ across $8\Omega$, independently confirming the result.