Question

Calculate 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

`\begin{gathered} R=\rho(L)/(A) \\ R=1.7*10^(-8)\frac{2.84\text{ m}}{0.0025132741\text{ m}^2} \\ R=1.9*10^(-5)\text{ ohm} \\ to\text{ convert into miliOhms , multiply by 1000} \\ R=R=\frac{1.9\text{ohm}}{10^(5)}*\frac{1000\text{ miliOhms}}{1\text{ Ohms}}=0.01921\text{ ohms} \end{gathered}`

therefore, the resistivity is 0.019210 miliOhms

Step-by-step explanation

Step 1

The resistance of a cylindrical segment of a conductor is equal to the resistivity of the material times the length divided by the area

`\begin{gathered} R=\rho(L)/(A) \\ where\text{ }\rho\text{ is the resistivity of the material} \\ L\text{ is the lenght} \\ A\text{ is the area} \end{gathered}`

so

Step 1

a)let

`\begin{gathered} \rho=1.7*10^(-8) \\ L=2.84 \\ diameter=\text{ 0.04 m} \\ Area\text{ = unknown} \end{gathered}`

bI find the area

the area of a circle is given by:

`area=\pi((diameter^2)/(4))`

so, replace

`\begin{gathered} area=\pi((0.04m^2)/(4)) \\ Area=0.0025132741\text{ m}^2 \end{gathered}`

c) now, we can replace the values in the formula

`\begin{gathered} R=\rho(L)/(A) \\ R=1.7*10^(-8)\frac{2.84\text{ m}}{0.0025132741\text{ m}^2} \\ R=1.9*10^(-5)\text{ ohm} \\ to\text{ convert into miliOhms , multiply by 1000} \\ R=R=\frac{1.9\text{ohm}}{10^(5)}*\frac{1000\text{ miliOhms}}{1\text{ Ohms}}=0.01921\text{ ohms} \end{gathered}`

therefore, the resistivity is 0.019210 miliOhms

I hope this helps yo u