Given:
• Diameter = 0.300 mm
,
• Resistance = 0.500 Ω
,
• Temperature = 20.0ºC
,
• Resistivity = 1.68 * 10⁻⁸ Ω*m
Let's find the length of the copper wire.
To find the length of the wire, apply the formula:
[tex]\begin{gathered} R=\frac{\rho L}{A} \\ \\ R=\frac{\rho L}{\pi r^2} \end{gathered}[/tex]
Where:
R is the resistance = 0.500 Ω
p is the resistivity = 1.68 * 10⁻⁸ Ω*m
L is the length
r is the radius = diameter/2 = 0.300mm/2 = 0.15 mm
Convert the radius to meters, where:
1 m = 1000 mm
0.15mm = 0.15 x 10⁻³ m
Now, input values into the formula and solve fo L:
[tex]0.500=\frac{1.68\times10^{-8}\times L}{\pi\times(0.15\times10^{-3})^2}[/tex]
Solving further, rewrite the equation for the length L:
[tex]\begin{gathered} L=\frac{0.500\pi\times(0.15\times10^{-3})^2}{1.68\times10^{-8}} \\ \\ L=\frac{3.534\times10^{-8}}{1.68\times10^{-8}} \\ \\ L=2.1\text{ m} \end{gathered}[/tex]
Therefore, the length of the copper wire is 2.1 meters.
ANSWER:
2.1 m
