Question

Determine the resistance, in milliOhms, of a metal rod 1.78 m long, 0.58cm diameter and composed of aluminum of resistivity 2.8 x 10-8 Ωm .

Answer 1

Given:

The length of the metal rod is,

$l=1.78\text{ m}$

The diameter of the aluminum rod is,

$\begin{gathered} d=0.58\text{ cm} \\ =0.58\times10^{-2}\text{ m} \end{gathered}$

The resistivity of aluminum is,

$\rho=2.8\times10^{-8}\text{ ohm.m}$

To find:

The resistance

Explanation:

The resistance of the material is,

$\begin{gathered} R=\frac{\rho l}{A} \\ Here,\text{ A=}\frac{\pi d^2}{4} \\ R=\frac{\rho l}{\frac{\pi d^2}{4}} \\ R=\frac{4\rho l}{\pi d^2} \end{gathered}$

Substituting the values we get,

$\begin{gathered} R=\frac{4\times2.8\times10^{-8}\times1.78}{\pi\times(0.58\times10^{-2})^2} \\ =1.88\times10^{-3}\text{ ohm} \\ =1.88\text{ mOhm} \end{gathered}$

Hence, the resistance is 1.88 mOhm.