a single layer of number 24 AWG (d0.0201 in) commercial iron wire is wound over a ceramic tube whose diameter is 3.25 inif the total wire resistance is 41 ohms, determine the number of turns.
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The diameter of the turns is 3.25 + 0.0201 inchesThe circumference of a turn is pi diameterFind the resistance per unit length from tables for iron wire, or from specific resistanceThe resistivity of iron is far from clear cut, as it depends on previous thermal history as well as impuritiesThe first link below gives it as 100 nΩ·m (nano-ohm-meters)From this work out the resistance for 24R specific resistance (length/Area) 10^-7 (1m / 2.05^-7m^2) 0.0000001 4878049 0.4878 ohms/m Another source (second link) gives it in traditional units (US mostly) of 57.81 ohm circular mil per footCircular mil is the cross sectional area in square mils (mil 1/1000 inch)For 24 wire area pi r^2 317.31 circular mil Resistance 57.81 / 317.3 0.1822 ohms/footThese don't closely agree because they are different types of ironThe second is closer to commercial iron whatever that might be, because it is low carbon steel, what most people call soft ironThe first is more or less pure iron, rarely found except in a laboratoryWork out the number of turns: First the total resistance / resistance per foot gives the total length in feetThen divide by the length per turn to get number of turnsI don't know what level you are at schoolThis does not take into account a slight increase in length per turn to allow for the thickness of insulation and the spiral shape of a turn that are considered in practiceYou could find the formula for spirals (helical coil) and add spacing between turns for insulationThis could increase diameterThere might be some length allowed for wire leading into the coil tooThese both mean slightly less turns than calculated above.
