temperature coefficient of resistance a. As a coil gets hot, its electrical resistance increases. The electrical conductivity at temperatures other then 20°C can be calculated as follows.
FIGURE 1.37 Helmholtz coil configuration: two identical coils in the XY plane, with radius a, and with an axial separation a equal to the radius.
The total wire diameter includes the thickness of the electrical insulation layer (usually a varnish coating) and is used to determine the coil size or the number of turns that will fit on a bobbin. The wire insulation thickness is specified by the number of insulation layers that are built up on the wire, such as single build and double build. The total insulated wire diameter can be calculated based on a curve fit of the tables from MWS Wire Industries (1985), as follows. These equations give the total insulated wire diameter in units of meters and are accurate to within ±4 percent over the wire size range of AWG 4 to 60.
The typical winding density n for a given wire can be calculated based on a square lay, assuming each wire uses a square region equal to its diameter. Coils are usually wound with much less precision, so a winding density factor C is included to account for voids caused by loose windings or terminations. The winding density factor typically varies from 0.70 up to 0.95, and has units of turns per unit cross-sectional area.
The maximum winding density can be achieved if the wires form a triangular or a hexagonal cross-section pattern. The maximum winding density nmax and the corresponding maximum winding density factor Cmax are shown here.
