Question

Question #0a80a

Answer 1

`L ~~ 2.356" meters"`

Explanation:

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"`