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.

Step-by-step explanation:

The expression for the resistivity is given by:

`\rho=(RA)/(l)`

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

`A=\pi((d)/(2))^2`

Substituting the value in the above equation, we get:

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

Rearrange the resistivity expression as:

`R=(\rho l)/(A)`

Substitute the values in the above equation, we get:

`\begin{gathered} R=\frac{1.7*10^(-8)\text{ }\Omega\text{m}*2.84\text{ m}}{0.00126\text{ m}^2} \\ \\ R=0.038*10^(-3)\text{ }\Omega \\ \\ R=0.038\text{ m}\Omega \end{gathered}`

Final Answer:

The resistance of a copper wire is 0.038 milliOhms.