Wire Size

How do you choose the wire diameter? Suppose you know the desired coil dimensions and want to achieve a certain coil resistance by filling that volume with wire.

Find Resistance, Given Coil Dimensions and Wire

Let's start with the basic equation for d.c. resistance of a coil:

R = (4 D T ω) / d^2

Substitute turns T = L l / d:

R = (4 D L l ω) / d^3

• R = resistance, ohms
• ω = resistivity, Ω cm
• L = coil length, cm
• D = coil diameter, cm
• d = wire diameter, cm
• T = turns
• l = layers
• πDT = wire length

Find Wire Diameter, Given Coil Dimensions and Resistance

Solve the above equation for d, wire diameter:

d = cube root( 4 D L l ω / R )

Note result goes as the cube of the wire diameter which makes diameter tolerance important.