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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.

An electric machine uses electromagnetism to transfer energy between electrical and mechanical forms, or between electrical circuits. An electric motor converts electrical input into mechanical output; an electrical generator converts mechanical input into electrical output. The wider machine category also includes the stationary electrical transformer. A rotating electric machine combines force on current-carrying conductors with electromagnetic induction; the same rotating conductors that develop torque can develop an opposing induced electric potential difference.^[ref]

For an original idealized direct current motor example, let $e=k_e\omega$, $\tau =k_{t}I$, and $V=e+IR$, where $e$ is the induced opposing electric potential difference, $\omega$ the angular velocity, $\tau$ the torque, and $R$ the winding electrical resistance. In coherent SI units, assume $k_e=k_t=0.1$, $\omega =100\mathrm{rad}{\mathrm{s}}^{-1}$, $I=2\mathrm{A}$, and $R=1\Omega$. Thenand the electromechanical conversion power balance isThe $20/24$ conversion fraction is about $83.3\%$ before friction and other losses. At rest the induced term vanishes, so applying the same $12\mathrm{V}$ gives $12\mathrm{A}$ in this simplified model. This makes the opposing induced electric potential difference experimentally visible: at fixed applied electric potential difference, a shaft-speed measurement and an electric current measurement distinguish a turning motor from its stalled state. Actual starting control and additional losses change the idealized numbers, not the need to balance electrical input, mechanical output, and heating.

Electromechanical conversion power balance applies conservation of energy to an electric machine's electrical and mechanical ports, internal storage and losses. In an electric motor sign convention, with electrical input positive and mechanical output positive,The internal term can include a changing magnetic field and rotational kinetic energy. Omitting it is justified only at the relevant steady operating point or after averaging over a cycle with no net storage change.

An original constant-field direct current motor model has winding electrical resistance $R$, inductance $L$, opposing induced electromotive force $e$, and current $i$:Multiplication by $i$ givesFor an ideal conversion coupling, $e=k_e\omega$ and electromagnetic torque ${\tau }_e=k_{t}i$ give $ei={\tau }_e\omega$ when the numerical constants agree in coherent SI units. The induced electrical term is converted power, not a resistive loss. DOE's motor analysis derives current from applied minus opposing induced electric potential difference and relates torque to field and armature current.^[ref]

Suppose $v=24\mathrm{V}$, $i=2\mathrm{A}$, $R=1\Omega$, $L=0.5\mathrm{H}$ and $di/dt=4\mathrm{A}{\mathrm{s}}^{-1}$. Then $e=20\mathrm{V}$ andThe terms are winding heating, increasing magnetic energy, and mechanical conversion. If $10\mathrm{W}$ is additionally going into rotational acceleration and mechanical losses are neglected, only $30\mathrm{W}$ reaches the shaft load at that instant. Calling all $40\mathrm{W}$ useful shaft output would omit a second storage term.

A proposed experiment records terminal electric potential difference, electric current, shaft speed and load torque during acceleration and after settling. The discrepancy between electrical input and load output can include storage as well as heating. For an electrical generator, reversing the port directions gives the corresponding mechanical-input balance; the physical energy accounting is unchanged.

Jeffrey Lang is an electrical engineer whose work concerns electromechanical conversion power balance, control and small-scale devices. MIT's Research Laboratory of Electronics identifies the same professor as Jeffrey H. Lang and describes research on electric motors, electrical generators and microelectromechanical systems, together with teaching in circuits and electromagnetism.^[ref]

The identified MIT profile provides an externally hosted portrait of Jeffrey H. Lang.

For an original motor-scale illustration, a shaft delivering torque $\tau =2\mathrm{mN}\mathrm{m}$ at angular velocity $\omega =1000\mathrm{rad}{\mathrm{s}}^{-1}$ delivers $P_m=\tau \omega =2\mathrm{W}$. If electrical input is $3\mathrm{W}$ and the operating point is steady, the remaining $1\mathrm{W}$ must be accounted for by losses or another specified output. During acceleration some input can instead increase rotational kinetic energy. Reporting only shaft speed would not establish either output power or conversion efficiency.

With Anant Agarwal, Lang is credited on the MIT course material State and Memory by Anant Agarwal and Jeffrey Lang. It explains how a capacitor's state summarizes the part of past input needed to predict its future response.^[ref] For a series RC circuit with a constant later input $V_f$,Two different earlier input histories that leave the same initial capacitor electric potential difference give the same subsequent response under the same future input. For stipulated $RC=1\mathrm{ms}$, $v_C(0)=1\mathrm{V}$ and $V_f=3\mathrm{V}$, the value after one time constant is $3-2/e\approx 2.2642\mathrm{V}$. This original numerical example shows what it means for the state to retain enough of the past without retaining the entire waveform.