Question

alculate the resistance in milliOhms of a copper wire 2.84 m long and 0.04 m diameter? The resistivity of copper is 1.7 x 10^-8.

Answer 1

Given:

The length of the copper wire is: l = 2.84 m.

The diameter of the copper wire is: d = 0.04 m.

The resistivity of the copper is: ρ = 1.7 x 10^-8 Ωm.

To find:

The resistance of the copper wire.

Explanation:

The expression for the resistivity is given by:

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

Here, A is the cross-sectional area of the copper wire, which is given by:

$A=\pi(\frac{d}{2})^2$

Substituting the value in the above equation, we get:

$\begin{gathered} A=\pi(\frac{0.04}{2})^2 \\ \\ A=0.00126\text{ m}^2 \end{gathered}$

Rearrange the resistivity expression as:

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

Substitute the values in the above equation, we get:

$\begin{gathered} R=\frac{1.7\times10^{-8}\text{ }\Omega\text{m}\times2.84\text{ m}}{0.00126\text{ m}^2} \\ \\ R=0.038\times10^{-3}\text{ }\Omega \\ \\ R=0.038\text{ m}\Omega \end{gathered}$

Final Answer:

The resistance of a copper wire is 0.038 milliOhms.