Answer to Question #282607 in Electric Circuits for Anonymous005

Question

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.

Answer 1

Solution

Given data are as below

Resistance of wire (R) =5$\Omega$

Radius of wire r=2.00mm

resistivity $\rho=1.68 \times 10^{-8}Ωm$

The resistance of any wire can written as

$R=\frac{\rho l}{A}$

Now then length of wire can be written as below formula

$l=\frac{RA}{\rho}$

Now putting all values

$l=\frac{5\times3.14\times(2\times10^{-3})^2}{1.68 \times 10^{-8}}$

$l=\frac{5\times3.14\times4\times10^{-6}}{1.68 \times 10^{-8}}$

$l=\frac{20\times3.14\times10^{2}}{1.68 }$

$l=\frac{62.8\times10^{2}}{1.68}\\l=3.74Km$

So length of wire is 3.74Km