Question #0a80a

1 Answer
Nov 29, 2016

Answer:

#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"#