Answer:
Length of the wire = 145.84 m
Step-by-step explanation:
Given : You wish to use #18 tungsten wire at 20°C to make a 10 Ω resistor.
To find : Length of wire will be required for this job.
Solution :
The #18 tungsten has a radius of [tex]r=5.1\times10^{-4}m[/tex].
The resistivity of the tungsten at 20° is [tex]\rho=5.6\times10^{-8}\Omega m[/tex].
The formula that relates resistance and resistivity is
[tex]R=\rho\frac{L}{\pi r^2}[/tex]
where L is the length of the wire, R is the resistor, [tex]\pi r^2[/tex] its section and [tex]\rho[/tex] is the resistivity .
Now, we can calculate L :
[tex]L=\frac{R\pi r^2}{\rho}[/tex]
[tex]L=\frac{(10)(3.14)(5.1\times10^{-4})^2}{5.6\times10^{-8}}[/tex]
[tex]L=\frac{816.714\times10^{-8}}{5.6\times10^{-8}}[/tex]
[tex]L=\frac{816.714}{5.6}[/tex]
[tex]L=145.84 m[/tex]
Therefore, Length of the wire = 145.84 m
