# Efficiency

## Copper loss

The forces acting inside electric motors are caused by magnetic fields being generated by electromagnetic coils. Those coils are made of wound insulated wires with a measurable resistance (super-conductive wires are rarely used). The resistance depends on the material, the temperature, the cross section area and the length of the wire as well as impureness and lattice defects. That resistance is described mathematically by the so called specific electrical resistance, volume resistivity or simply resistivity with the Greek letter ρ (rho) used as symbol.
Omitting the influence of the temperature we get for the resistance of a metallic conductor: Where is:
R - ohmic resistance, ρ - resistivity, l - length of the wire, A - cross section area

Consequently the resulting unit is Ω * m (ohm * meters).
The reciprocal value of the resistivity (1 / ρ) is called electrical conductivity or specific conductance.
To make the resistance of electromagnets as low as possible, the used wire should have a large cross section area, it should not be longer than absolutely necessary and the resistivity should be as low as possible.

 Specific electrical resistance of some metalls Material Resistivity in Ω * mm2 / m Temperature coefficient in 1/K Silver 1,587 * 10-2 3,8 * 10-3 Copper (pure) 1,678 * 10-2 3,9 * 10-3 Gold 2,214 * 10-2 3,9 * 10-3 Aluminum 2,65 * 10-2 3,9 * 10-3 Brass (Copper & Zinc) 7 * 10-2 1,5 * 10-3 Platinum 1,05 * 10-1 3,8 * 10-3 Iron 1,0 * 10-1 to 1,5 * 10-1 5,6 * 10-3 Lead 2,08 * 10-1 4,2 * 10-3

At the table above, which is from Wikipedia, you can see that copper is an excellent metallic conductor. Silver is slightly better, but the price for this resource is clearly higher. Apart from some special cases, copper is used as core material of wires. That's why the losses caused by the wire of electromagnets are called copper loss.
You can read the temperature dependencies at the table, too. The temperature coefficient (unit symbol α, unit K-1) gives the increase of the resistivity if the temperature is rising for 1K.

## Core loss

To magnify the strength of magnetic fields inside electromagnets, core materials with a high permeability are used. At the chapter about permeability we saw, that iron is an adequate core material. The loss caused by effects of the core material are called iron loss or core loss. There are two significant factors leading to core losses:
1.) Hysteresis loss:
At the chapter hysteresis loop we saw that energy is needed to change the magnetization of ferromagnetic materials. To reduce those kind of losses, the core material should be magnetically soft (like soft iron), leading to a narrow, tiny area covered by the hysteresis loop.
2.) Eddy current loss:
The formation of eddy currents has been treated at one of the previous chapters. They occur inside the core material whenever the magnetization, thus the current through the windings of the coil varries. The currents running through the core material are transformed to heat and the magnetization of eddy currents counteract the desired change of magnetization. Eddy currents can be reduced by using many tiny, insulated iron particles instead of a massive core. The occurrence of large-scaled eddy currents can be inhibited by using laminated core materials with layers being insulated from each other by a lacquer coating. The axis of the iron sheets are oriented in parallel to the axis of the coil, because the eddy currents are running in the plane being perpendicular to it. Sometimes coated grains of iron are used to squeeze mold the core material.

## Energy conversion efficiency

The ratio between the useful output power and the input power is called energy conversion efficiency: Where is:
η - energy conversion efficiency, Pout - useful output power, Pin - input power

The symbol used for the energy conversion efficiency is the Greek letter η (eta). It is a dimensionless number between 0 and 1 and is sometimes given in percent (1=100%). A value of zero means that all of the input power is transformed into heat and no mechanical output power is delivered by the electric motor. An electric motor with an energy conversion efficiency of 1 would be a very fine thing, but is just wishful thinking. The copper and core losses described above are inevitably and it is the destination to use a design coming as close as possible to 100%.