Question

Determine the resistance, in milliOhms, of a metal rod 2.39 m long, 0.47cm diameter and composed of aluminum of resistivity 2.8 x 10-8 Ωm .

Answer 1

0.965 mililΩ

Explanation

The resistance of a metal rod depends on resistivy, length and temperature, it can fe found usign the formula

$\begin{gathered} R=\rho\frac{L}{A} \\ where\rho\text{ is} \\ L\text{ is the length } \\ A\text{ is the seccion of area} \end{gathered}$

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Step 1

a) let

$\begin{gathered} \rho=2.8*10^{-8}m\text{ ^^^^2126} \\ L=2.39\text{ m} \\ d=0.4\text{ cm=0.4 cm\lparen}\frac{1m}{100\text{ cm}}\text{\rparen=0.0047 m} \end{gathered}$

b) find the transversal area (A)

use the area of a circle

$\begin{gathered} A=\pi r^2 \\ replace \\ A=\pi(0.0047\text{ m\rparen}^2 \\ A=6.93*10^{-5}m^2 \end{gathered}$

c) now, replace in the formula

$\begin{gathered} R=\rho\frac{L}{A} \\ R=2.8*10^{-8}m\text{ ^^^^2126*}\frac{2.39\text{ m}}{6.93*10^{-5}m^2} \\ R=0.00096565\text{ ^^^^2126} \end{gathered}$

finally, to convert into milliOhms, Multiply by 1000

$\begin{gathered} R=0.000965365*1000\text{ m^^^^2126} \\ R=0.965\text{ m^^^^2126} \end{gathered}$

therefore, the answer is

0.965 miliΩ

I hope this helps you