Question

Determine the resistance, in milliOhms, of a metal rod 2.96 m long, 0.89cm diameter and composed of aluminum of resistivity 2.8 x 10-8 Ωm .

Answer 1

The resistance R of a rod with length L, cross-sectional area A and resistivity ρ is given by:

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

On the other hand, the area of a circle with diameter D is given by:

`A=(\pi)/(4)D^2`

Then, the resistivity of the rod in terms of its diameter is:

`R=(4\rho L)/(\pi D^2)`

Replace L=2.96m, D=0.89cm and ρ=2.8×10^(-8)Ωm to find the resistance of the metal rod:

`\begin{gathered} R=(4\rho L)/(\pi D^2) \\ \\ =(4(2.8*10^(-8)\Omega m)(2.96m))/(\pi(0.89cm)^2) \\ \\ =(4(2.8*10^(-8)\Omega m)(2.96m))/(\pi(0.89*10^(-2)m)^2) \\ \\ =1.332232...*10^(-3)\Omega \\ \\ \approx1.33m\Omega \end{gathered}`

Therefore, the resistance of the metal rod is approximately 1.33 miliOhms.