= Electric machine
{wiki}
= Electrical machine
{synonym}
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>.<DOE Fundamentals Handbook Electrical Science>[Volume 2, Module 6, DC Motor Theory; Volume 4, Module 13, Transformer Theory]{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 $k_e=k_t=0.1$, $\omega=100\,\mathrm{rad\,s^{-1}}$, $I=2\,\mathrm A$, and $R=1\,\Omega$. Then
$$
e=10\,\mathrm V,\qquad \tau=0.2\,\mathrm{N\,m},\qquad V=12\,\mathrm V,
$$
and the <electromechanical conversion power balance> is
$$
VI=24\,\mathrm W
=\underbrace{\tau\omega}_{20\,\mathrm W}+\underbrace{I^2R}_{4\,\mathrm W}.
$$
The $20/24$ 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.
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