# Can you explain all the physics rules behind the functioning of an electric motor including how to calculate it's energy efficiency.

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An electric motor is a device that transforms the electric energy into mechanic energy. It does this by transforming the electric energy into a, so called, rotating a magnetic filed (of the rotor for example). This rotating magnetic field, interacts with a static external magnetic field, (of the stator), creating a torque, that starts to rotate the rotor. The energy efficiency is computed by the following relation

Efficiency = Available mechanical power/Absorbed electric power

`eta = P_("out")/P_("in")`

`P_("in")` is simply the apparent power (vectorial sum of real power and reactive power)

`P_("in") =U*I`

From this, a part of it is lost on the complex reactance of the inductor that makes the rotor. The rest (real power, or power on resistance of rotor) is used to produce mechanical torque).

`P =U*I*cos(theta) = U^2/R = I^2*R`

From this power a part is lost because of friction forces. Thus the mechanical power is

`P_("out") = P -P_("friction") = U*I*cos(theta)-P_("friction")`

Thus the efficiency becomes

`eta = (U*I*cos("theta") -P_("friction"))/(U*I) =cos(theta) -P_("friction")/(U*I)`

The efficiency is higher for smaller `theta` angles and friction.