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Electricity generation converts another form of energy into electrical energy supplied to an electrical load or electric power system. A rotating electrical generator uses electromagnetic induction; a solar cell instead converts incident radiation through the photovoltaic effect. Neither process creates energy. The relevant input and output boundaries determine which losses enter a quoted conversion fraction.

For an original ideal rotating-coil model, let $N$ turns of area $A$ rotate at constant angular velocity $\omega$ in a uniform magnetic field $B$. With the coil normal initially aligned with that field, the linked magnetic flux and induced electromotive force areFor $N=100$, $A=0.01{\mathrm{m}}^2$, $B=0.5\mathrm{T}$ and $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$, the peak is $50\mathrm{V}$ and the sinusoidal root mean square value is $50/\sqrt{2}\approx 35.36\mathrm{V}$. Doubling the speed doubles both the amplitude and frequency in this model. The DOE exposition develops the rotating-conductor waveform and distinguishes peak from effective values.^[ref]

An open-circuit induced electric potential difference does not specify deliverable power. On connecting a load, the resulting electric current produces an opposing electromagnetic torque; sustained electrical output requires corresponding mechanical input and provision for losses. For a stipulated steady shaft input of $2.0\mathrm{kW}$ and combined losses of $0.2\mathrm{kW}$, output is $1.8\mathrm{kW}$ and the shaft-to-electrical conversion fraction is $0.9$. This fraction excludes any earlier conversion from fuel or another primary supply into shaft power.

A proposed demonstration couples a small electrical generator to a controllable drive, measures rotational speed and open-circuit waveform, then applies several known electrical loads while recording shaft torque, electric current and terminal electric potential difference. The additional mechanical effort under load tests the electromechanical conversion power balance; an open-circuit waveform alone cannot test that balance.

A solar cell uses the photovoltaic effect to turn photon energy into electrical work. In a semiconductor, above-gap photon absorption generates an electron in the conduction band and an electron hole in the valence band. A p-n junction, together with selective electrical contacts, collects the two carrier species at opposite terminals. Carrier diffusion and the built-in electric field help separate them before electron-hole recombination. Illumination maintains different quasi-Fermi levels for electrons and electron holes; their splitting, divided by $e$, sets the available terminal voltage in an ideal device. The equilibrium built-in potential alone cannot continuously deliver work.

For an ideal junction, the illuminated output current density isHere $J_{\mathrm{sc}}$ is the photogenerated short-circuit current density and $J_0$ the diode saturation current. The useful operating point maximizes $VJ$, rather than either current or voltage separately. With solar-cell fill factor $\mathrm{FF}=P_{\max }/(V_{\mathrm{oc}}{I}_{\mathrm{sc}})$,Series resistance, shunts, incomplete photon absorption and nonradiative recombination reduce the attainable efficiency.

The Shockley-Queisser limit removes these avoidable losses but retains the following physical constraints. There is one semiconductor junction with one band gap; each absorbed above-gap photon yields at most one collected electron-hole pair; carriers thermalize to the cell temperature; and the inverse optical process produces unavoidable radiative recombination. If ${\Phi }_{\odot }(E)$ is the incident photon flux per unit energy, ideal photon absorption givesThe same ability to absorb light requires the junction to emit it. At a forward voltage $V$, the emitted photon population has a chemical potential $eV$; in the ordinary nondegenerate limit the resulting recombination current is the exponential diode term above. Maximizing $VJ$ with this radiative $J_0$, and then choosing $E_g$, gives the limiting efficiency.

A small band gap collects many photons but gives a low voltage and large thermalization losses. A large band gap permits a larger voltage but transmits too much of the incident spectrum. Below-gap photons are lost to transmission, excess photon energy above the gap becomes heat, and radiative emission and its associated entropy loss keep $e{V}_{\mathrm{oc}}$ below $E_g$. The optimum single-junction conversion is roughly thirty percent under ordinary unconcentrated sunlight; the precise ceiling depends on spectrum, cell temperature and optical geometry. The original detailed-balance calculation gave about $30\%$ at $E_g\simeq 1.1\mathrm{eV}$ under its specified assumptions.^[ref] Multiple junctions and optical concentration change the assumptions and consequently change the bound.

The photovoltaic effect is the production of an electric potential difference or an electric current by photon absorption in a material or device. In a semiconductor, absorbed photons generate electrons and electron holes; asymmetric transport and selective collection can maintain distinct quasi-Fermi levels and deliver electrical power to a load. An equilibrium built-in potential alone supplies no continuous electrical power.

A solar cell converts incident light into electrical power through the photovoltaic effect. A semiconductor p-n junction separates and collects photogenerated electrons and electron holes. An ideal illuminated junction has output current densityHere $J_{\mathrm{sc}}$ is the short-circuit current density, $J_0$ is the diode saturation current, and $V_{\mathrm{oc}}$ is the open-circuit electric potential difference. The conversion efficiency is the largest delivered $VJ$ divided by the incident power per unit area; the short-circuit and open-circuit operating points themselves deliver zero power.