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Answer 1 · 2016-11-29T18:38:12

$L ~~ 2.356" meters"$

The resistance, R, of a wire resistor (in Ohms) is:

$R = rhoL/A" [1]"$

where $rho$ is the resistivity (in Ohm•meters), A is the cross-sectional area of the wire (in meters²) and L is the length of the wire:

Solve equation [1] for L:

$L = (RA)/rho" [2]"$

I believe that there is a minor error the unit for resistivity should be $Omega•meter$ not $Omega/(meter)$

We are given: $rho = 5xx10^-7Omega•m and R = 6 Omega$

Convert the diameter to a a radius (in meters)

$r = 2.5 xx 10^-4m$

The cross-sectional area is that of a circle:

$A = pir^2$

$A = 6.25xx10^-8pim^2$

Substitute into equation [2]:

$L = ((6 Omega)(6.25xx10^-8pim^2))/(5xx10^-7Omega*m)$

Please notice how the unit cancel, leaving only meters:

$L ~~ 2.356" meters"$