Answer to Question #282607 in Electric Circuits for Anonymous005

Question #282607

The resistivity is 1.68 x 10^-8 Ωm. Calculate the length of a copper wire with diameter 4.00 mm that has a resistance of 5.00 Ω. Ans: 3.74 km.


1
Expert's answer
2021-12-28T10:52:55-0500

Solution

Given data are as below

Resistance of wire (R) =5Ω\Omega

Radius of wire r=2.00mm

resistivity ρ=1.68×108Ωm\rho=1.68 \times 10^{-8}Ωm

The resistance of any wire can written as

R=ρlAR=\frac{\rho l}{A}

Now then length of wire can be written as below formula

l=RAρl=\frac{RA}{\rho}

Now putting all values

l=5×3.14×(2×103)21.68×108l=\frac{5\times3.14\times(2\times10^{-3})^2}{1.68 \times 10^{-8}}

l=5×3.14×4×1061.68×108l=\frac{5\times3.14\times4\times10^{-6}}{1.68 \times 10^{-8}}

l=20×3.14×1021.68l=\frac{20\times3.14\times10^{2}}{1.68 }

l=62.8×1021.68l=3.74Kml=\frac{62.8\times10^{2}}{1.68}\\l=3.74Km

So length of wire is 3.74Km



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